In the diagram given, quadrilaterals ABGF and GEDC are parallelogra...

Question
In the diagram given, quadrilaterals ABGF and GEDC are parallelograms, where B - G - C and F - G - E (betweenness).
Prove: mArcAB + mArcCD = 120.
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First of all something about the center of the circle. Go to the midpoint of AB, draw the line L perpendicular to AB through the midpoint. This line L contains the center. Similarly go to the midpoint of CD and go up by the perpendicular line M. This line M again contains the center.
Since AB and CD are parallel, so will be L and M.
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      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (292μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • creating: site.layouts.app (486μs)
      • composing: site.layouts.app (25μs)
      • creating: components.canonical (640μs)
      • composing: components.canonical (107μs)
      • creating: components.open-graph (214μs)
      • composing: components.open-graph (128μs)
      • creating: site.headers.header (387μs)
      • composing: site.headers.header (81μs)
      • Illuminate\Cache\Events\CacheHit (2.81ms)
      • creating: components.footer (314μs)
      • composing: components.footer (106μs)
      • Illuminate\Cache\Events\CacheHit (1.06ms)
      • Illuminate\Cache\Events\CacheMissed (351μs)
      • Illuminate\Database\Events\StatementPrepared (767μs)
      • Illuminate\Database\Events\QueryExecuted (1.56ms)
      • eloquent.retrieved: App\Models\SubjectCat (99μs)
      • Illuminate\Cache\Events\KeyWritten (372μs)
      • Illuminate\Cache\Events\CacheHit (316μs)
      • Illuminate\Cache\Events\CacheHit (274μs)
      • Illuminate\Cache\Events\CacheHit (152μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • Illuminate\Cache\Events\CacheHit (303μs)
      • Illuminate\Cache\Events\CacheHit (331μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (268μs)
      • creating: components.forms.contact-us (351μs)
      • composing: components.forms.contact-us (351μs)
      • creating: components.forms.get-started (199μs)
      • composing: components.forms.get-started (91μs)
      • creating: components.forms.free-tool-download (235μs)
      • composing: components.forms.free-tool-download (81μs)
      • creating: components.forms.claim-free-worksheet (181μs)
      • composing: components.forms.claim-free-worksheet (80μs)
      • creating: components.forms.tutor-subscription-waitlist (158μs)
      • composing: components.forms.tutor-subscription-waitlist (77μs)
      • creating: components.forms.tutor-subscription-join (145μs)
      • composing: components.forms.tutor-subscription-join (77μs)
      • creating: components.forms.tutor-support (136μs)
      • composing: components.forms.tutor-support (72μs)
      • 311 x Illuminate\Cache\Events\CacheHit (18.16%)
        94.29ms
        20 x Illuminate\Database\Events\StatementPrepared (6.19%)
        32.16ms
        20 x Illuminate\Database\Events\QueryExecuted (5.5%)
        28.56ms
        11 x Illuminate\Cache\Events\CacheMissed (1.97%)
        10.21ms
        11 x Illuminate\Cache\Events\KeyWritten (1.19%)
        6.16ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (0.91%)
        4.70ms
        1 x Illuminate\Database\Events\ConnectionEstablished (0.33%)
        1.70ms
        1 x Illuminate\Routing\Events\Routing (0.32%)
        1.66ms
        12 x eloquent.retrieved: App\Models\SubjectCat (0.24%)
        1.25ms
        1 x Illuminate\Routing\Events\RouteMatched (0.18%)
        942μs
        1 x creating: components.canonical (0.12%)
        640μs
        1 x creating: site.layouts.app (0.09%)
        486μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.09%)
        469μs
        1 x creating: homework.show (0.09%)
        469μs
        1 x creating: site.headers.header (0.07%)
        387μs
        1 x creating: components.forms.contact-us (0.07%)
        351μs
        1 x composing: components.forms.contact-us (0.07%)
        351μs
        1 x creating: components.breadcrumbs (0.07%)
        347μs
        1 x creating: components.footer (0.06%)
        314μs
        6 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.06%)
        300μs
        1 x eloquent.booting: App\Models\SubjectCat (0.06%)
        294μs
        1 x creating: components.forms.free-tool-download (0.05%)
        235μs
        1 x creating: components.open-graph (0.04%)
        214μs
        2 x eloquent.retrieved: App\Models\Subject (0.04%)
        201μs
        1 x composing: homework.show (0.04%)
        201μs
        1 x creating: components.forms.get-started (0.04%)
        199μs
        1 x creating: components.forms.claim-free-worksheet (0.03%)
        181μs
        1 x composing: components.breadcrumbs (0.03%)
        173μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.03%)
        170μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.03%)
        159μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.03%)
        158μs
        1 x creating: components.forms.tutor-subscription-join (0.03%)
        145μs
        1 x creating: components.forms.tutor-support (0.03%)
        136μs
        1 x composing: components.open-graph (0.02%)
        128μs
        1 x eloquent.booting: App\Models\Subject (0.02%)
        127μs
        1 x composing: components.canonical (0.02%)
        107μs
        1 x composing: components.footer (0.02%)
        106μs
        1 x composing: components.forms.get-started (0.02%)
        91μs
        1 x composing: site.headers.header (0.02%)
        81μs
        1 x composing: components.forms.free-tool-download (0.02%)
        81μs
        1 x composing: components.forms.claim-free-worksheet (0.02%)
        80μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.01%)
        77μs
        1 x composing: components.forms.tutor-subscription-join (0.01%)
        77μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        75μs
        1 x composing: components.forms.tutor-support (0.01%)
        72μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        58μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        42μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        38μs
        1 x composing: site.layouts.app (0%)
        25μs
      14 templates were rendered
      • 1x homework.showshow.blade.phpblade
      • 1x components.breadcrumbsbreadcrumbs.blade.phpblade
      • 1x site.layouts.appapp.blade.phpblade
      • 1x components.canonicalcanonical.blade.phpblade
      • 1x components.open-graphopen-graph.blade.phpblade
      • 1x site.headers.headerheader.blade.phpblade
      • 1x components.footerfooter.blade.phpblade
      • 1x components.forms.contact-uscontact-us.blade.phpblade
      • 1x components.forms.get-startedget-started.blade.phpblade
      • 1x components.forms.free-tool-downloadfree-tool-download.blade.phpblade
      • 1x components.forms.claim-free-worksheetclaim-free-worksheet.blade.phpblade
      • 1x components.forms.tutor-subscription-waitlisttutor-subscription-waitlist.blade.phpblade
      • 1x components.forms.tutor-subscription-jointutor-subscription-join.blade.phpblade
      • 1x components.forms.tutor-supporttutor-support.blade.phpblade
      uri
      GET college-homework-library/{category}/{subject}/{id}
      middleware
      web, utm.parameters
      controller
      App\Http\Controllers\HomeworkLibraryController@show
      namespace
      where
      as
      homework.show
      file
      app/Http/Controllers/HomeworkLibraryController.php:79-176
      20 statements were executed, 5 of which were duplicates, 15 unique. Show only duplicated39.8ms
      • Connection Establishedtwenty4_siteHomeworkLibraryController.php#91
        Backtrace
        • 13. app/Http/Controllers/HomeworkLibraryController.php:91
        • 14. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 15. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 16. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary` where `status` = 'published' and `price` > 0 and `solutionslibrary`.`id` = '11323' limit 1
        11.04mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 11323
        Backtrace
        • 16. app/Http/Controllers/HomeworkLibraryController.php:97
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subjects` where `subjects`.`id` in (3)
        1.11mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` in (11323)
        1.26mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1.24mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 1
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `solutionslibrary` where `id` <> 11323 and `subject` = 3 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        4mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 11323
        • 1: 3
        • 2: published
        • 3: 0
        Backtrace
        • 14. app/Repositories/HomeworkLibraryRepository.php:30
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Repositories/HomeworkLibraryRepository.php:39
        • 19. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `subjects` where `subjects`.`id` in (3)
        1mstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Repositories/HomeworkLibraryRepository.php:39
        • 24. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 11323 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.29mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 11323
        • 1: question
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 11323 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        1.13mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 11323
        • 1: teaser
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:69
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
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        1.18mstwenty4_siteHomeworkLibrary.php#260
        Bindings
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        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:80
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1.29mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 1
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 32. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 33. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 34. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
        • 35. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1.38mstwenty4_siteSubject.php#100
        Bindings
        • 0: 1
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1
        4.24mstwenty4_siteSubject.php#100
        Bindings
        • 0: 3
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 4 limit 1
        1.14mstwenty4_siteSubject.php#100
        Bindings
        • 0: 4
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        1.41mstwenty4_siteSubject.php#100
        Bindings
        • 0: 10
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 33 limit 1
        1.19mstwenty4_siteSubject.php#100
        Bindings
        • 0: 33
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 11 limit 1
        1.2mstwenty4_siteSubject.php#100
        Bindings
        • 0: 11
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 5 limit 1
        1.08mstwenty4_siteSubject.php#100
        Bindings
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        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 34 limit 1
        1.06mstwenty4_siteSubject.php#100
        Bindings
        • 0: 34
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 31 limit 1
        1.22mstwenty4_siteSubject.php#100
        Bindings
        • 0: 31
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 36 limit 1
        1.34mstwenty4_siteSubject.php#100
        Bindings
        • 0: 36
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 28. view::components.footer:170
      App\Models\SubjectCat
      12SubjectCat.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      6HomeworkLibraryFile.php
      App\Models\Subject
      2Subject.php
          _token
          Gxf8u9HZDJDdpqa6UbgUH5hsoIga7HB3EQOuZe76
          utm_source
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          redirectUrl
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          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Mathematics/Geo...
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          PHPDEBUGBAR_STACK_DATA
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          status_code
          200
          
          status_text
          OK
          format
          html
          content_type
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          request_query
          []
          
          request_request
          []
          
          request_headers
          0 of 0
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          request_cookies
          []
          
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