Wednesday, September 4, 2013

Problem 916: Cyclic Quadrilateral, Three Circles, Diameter, Congruence

Geometry Problem
Post your solution in the comment box below
Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to see the complete problem 916.

Online Geometry Problem 916: Cyclic Quadrilateral, Three Circles, Diameter, Congruence.

Posted by Antonio Gutierrez at 7:52 AM
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2 comments:

  1. UnknownSeptember 4, 2013 at 11:43 AM

    draw DF,EA,AC and BD
    AEB=CFD=ACD=DBA=90
    CDA=EBA, BAD=FCD
    EBA~CDA =>AD=AB*DC/EB
    ABD~CFD =>AD=CD*AB/CF
    CD*AB/EB=CD*AB/CF
    CF=EB

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  2. Peter TranSeptember 4, 2013 at 5:11 PM

    http://img62.imageshack.us/img62/4753/c84r.png
    Connect DF and AE and note that DE and AE perpendicular to BC
    Let M is the projection of O over BC
    We have M is midpoint of BC and EF => BE=CF

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