## 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.

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

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

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

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.