Geometry Geometry Math Forum

 November 1st, 2019, 08:53 AM #1 Senior Member   Joined: Mar 2015 From: Universe 2.71828i3.14159 Posts: 169 Thanks: 65 Math Focus: Area of Circle Geometry Problem Series, Question 3: Pentagon $ABCDE$ is inscribed in a circle. $AB \parallel EC$, $AE \parallel BD$. $AD \cap EC \equiv G$, $BD \cap EC \equiv F$ and $AC \cap BD \equiv H$. Prove that the area of $AGFH$ is equal to the sum of the areas of $DEG$ and $BCH$. --------  November 1st, 2019, 09:11 AM #2 Senior Member   Joined: Jun 2019 From: USA Posts: 386 Thanks: 211 Do you mean AGFH? November 1st, 2019, 10:00 AM   #3
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Math Focus: Area of Circle
Quote:
 Originally Posted by DarnItJimImAnEngineer Do you mean AGFH?
Quadrilateral $AGFH$.

Triangles $DEG$ and $BCH$. November 1st, 2019, 10:11 AM #4 Senior Member   Joined: Jun 2019 From: USA Posts: 386 Thanks: 211 Yeah, I think it said AFGH before you fixed it, unless I was just having a dyslexic moment. On a side note, if we solve Question 1, 2, and 3, do we unlock the secrets of alchemy? (Couldn't resist. ) November 1st, 2019, 12:38 PM   #5
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Joined: Mar 2015
From: Universe 2.71828i3.14159

Posts: 169
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Math Focus: Area of Circle
Quote:
 Originally Posted by DarnItJimImAnEngineer Yeah, I think it said AFGH before you fixed it unless I was just having a dyslexic moment. On a side note, if we solve Questions 1, 2, and 3, do we unlock the secrets of alchemy? (Couldn't resist. )
No, but you will unlock the secret of the geometry of the Multiverse...    November 1st, 2019, 10:34 PM #6 Global Moderator   Joined: Dec 2006 Posts: 21,124 Thanks: 2332 $\small\triangle$BFG = $\small\triangle$AFG = $\small\triangle$ADF - $\small\triangle$DFG = $\small\triangle$DEF - $\small\triangle$DFG = $\small\triangle$DEG Area(AGFH) = $\small\triangle$ACG - $\small\triangle$CFH = $\small\triangle$BCG - $\small\triangle$CFH = $\small\triangle$BFG + $\small\triangle$BCH = $\small\triangle$DEG + $\small\triangle$BCH Tags geometry, problem, question, series Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post tahirimanov19 Geometry 1 November 1st, 2019 05:55 PM tahirimanov19 Geometry 0 November 1st, 2019 08:24 AM wuzhe Math Events 9 February 8th, 2013 11:58 AM Beevo Calculus 6 September 11th, 2012 04:13 PM Beevo Calculus 4 September 11th, 2012 02:13 PM

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