Tuesday, June 18, 2013

Problem 890: Two Squares inscribed in Circles, Concurrent Lines

Geometry Problem. GeoGebra, HTML5 Animation for iPad and Nexus.
Post your solution in the comments box below.

Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to see the dynamic geometry demostration of problem 890.

Online Geometry Problem 890: Two Squares inscribed in Circles, Concurrent Lines. GeoGebra, HTML5 Animation for iPad and more tablets

4 comments:

  1. This problem is the same as problem 772 with dynamic Geometry . See below for detail

    http://gogeometry.blogspot.com/2012/01/problem-722-squares-circumscribed.html

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    Replies
    1. Dear Peter problem 890 has more conclusions than problem 772

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  2. http://img834.imageshack.us/img834/6712/8rc.png
    Since BD and DF are diameters of circles O and O’ so ∠(BPD)= ∠(DPF)= 90
    So B, P and E are collinear.
    We have ∠(CPB)= ∠(FPG)= 45 ( angles face 90 degrees arc)
    So C, P, G are collinear.
    Since AC and EG are diameters of circles O and O’ => AP ⊥ CPG and PE ⊥ CPG
    So A,E and P are collinear

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  3. Let AE and CG intersect at a point Q, then we need to prove that Q,D,A,C,B concylic.
    ∠QAD = ∠EAD = arctan(ED/AD) = arctan(DG/CD) = ∠GCD = ∠QCD
    So Q,D,A,C concylic and the result follows.

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