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Question With May 2019 Division M Problem 2

 
 
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Re: Question With May 2019 Division M Problem 2
ReynosoDavid - 2019年05月8日 Wednesday 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.