
Geometry Geometry Math Forum 
 LinkBack  Thread Tools  Display Modes 
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 
Senior Member Joined: Mar 2015 From: Universe 2.71828i3.14159 Posts: 169 Thanks: 65 Math Focus: Area of Circle  
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 
Senior Member Joined: Mar 2015 From: Universe 2.71828i3.14159 Posts: 169 Thanks: 65 Math Focus: Area of Circle  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  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Geometry Problem Series, Question 1:  tahirimanov19  Geometry  1  November 1st, 2019 05:55 PM 
Geometry Problem Series, Question 2:  tahirimanov19  Geometry  0  November 1st, 2019 08:24 AM 
AMC 10A question 22 Geometry Problem  wuzhe  Math Events  9  February 8th, 2013 11:58 AM 
Problem with a PSeries Question  Beevo  Calculus  6  September 11th, 2012 04:13 PM 
Question on Series Problem  Beevo  Calculus  4  September 11th, 2012 02:13 PM 