Monday, May 19, 2008

Elearn Geometry Problem 74



See complete Problem 74
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 9:50 PM
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2 comments:

  1. c .t . e. oFebruary 27, 2010 at 1:33 PM

    Ang MBE = ang EAM = α ( have same arc EFM )

    ang EAH = ang EDH ( have same arc EH, AEHD concyclic )

    α = ß

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  2. MarcoDecember 12, 2022 at 7:41 PM

    [Here I am using a for alpha and b for beta]
    From Problem 73, we know that AEHD is a cyclic quad
    So <EAH=<EDH=b (< in same seg.)

    Consider triangle AEB
    b+<AEB+<MAB+<EBA=180
    b=180-<AEB-<MAB-<EBA-------(1)

    Consider triangle MAB
    <MAB+<AMB+<EBA+a=180
    a=180-<AMB-<MAB-<EBA---------(2)

    Since <AEB=<ABM (< in same seg)
    So (1)=(2)

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