Online Geometry theorems, problems, solutions, and related topics.
See complete Problem 73Three Intersecting Circles, Cyclic Quadrilateral, Angles. Level: High School, SAT Prep, College geometryPost your solutions or ideas in the comments.
Thanks for the beautiful problem!It 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...)A + F1 = 180, F2 + C1 = 180, C2 + H = 180A + H = 180 - F1 + 180 - C2A + H = 360 - F1 - C2A + H = 360 - ( 180 - F2 ) - ( 180 - C1 )A + H = F2 + C1A + H = 180 - C1 + C1A + 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.