Monday, May 19, 2008

Elearn Geometry Problem 73



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.

Posted by Antonio Gutierrez at 9:49 PM
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4 comments:

  1. AnonymousJune 5, 2008 at 5:31 AM

    Thanks for the beautiful problem!
    It works also if EFGH are on a circle instead of a line.. but don't know why... :-(
    Ciao

    ReplyDelete
  2. c .t . e. oJanuary 19, 2010 at 1:12 PM

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

    A + 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

    ReplyDelete
  3. Nilton LapaApril 21, 2012 at 10:30 AM

    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.

    ReplyDelete
  4. MarcoDecember 12, 2022 at 2:15 AM

    Join BF & CF
    <EAB=180-<CHD
    Similarly <AEF=180-<HDC
    So AEHD is a cyclic quad

    ReplyDelete

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