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Question With May 2019 Division M Problem 2

 
 
Chen Roger的相片
Question With May 2019 Division M Problem 2
由Chen Roger發表於2019年 05月 8日(Wed) 16:25
 

Hi all, 

    In the solution, it states that triangle CGI is isosceles because CG = DI. I know that it probably meant that CG = CI, but even then, how is CG = CI? I'm just curious. 

      Thanks, 

               Roger Chen

 
Reynoso David的相片
Re: Question With May 2019 Division M Problem 2
由Reynoso David發表於2019年 05月 8日(Wed) 19:05
 

Hew Roger!

That was indeed a typo. It is now fixed. Thanks for letting us know!

As to why the statement is true, consider the following: $CA$ is parallel to line $DE$ (since $\triangle ABC$ is isosceles, and we can look at their angles). Then we can reflect pentagon $ABCDE$ through line $CA$ to obtain the following diagram:


Then both $CG$ and $CI$ are lines that join opposite vertices of two adjacent regular pentagons of the same size, and therefore have the same length.

 
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