See complete Problem 73

Three Intersecting Circles, Cyclic Quadrilateral, Angles. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

## Monday, May 19, 2008

### Elearn Geometry Problem 73

Labels:
angle,
circle,
cyclic quadrilateral

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Thanks for the beautiful problem!

ReplyDeleteIt works also if EFGH are on a circle instead of a line.. but don't know why... :-(

Ciao

join F to B, C to G ( name F1, C1 on the left...)

ReplyDeleteA + F1 = 180, F2 + C1 = 180, C2 + H = 180

A + H = 180 - F1 + 180 - C2

A + H = 360 - F1 - C2

A + H = 360 - ( 180 - F2 ) - ( 180 - C1 )

A + H = F2 + C1

A + H = 180 - C1 + C1

A + H = 180

Using to circles 4 and 5 the statement proved in problem 72, we can say that BF and CH are paralel, so ang(EFB) = ang(GHD). Angles EAB and EFB are supplementary, so angles EAB and GHD are supplementary. That means that AEHC is cyclic.

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