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.

## Tuesday, June 18, 2013

### Problem 890: Two Squares inscribed in Circles, Concurrent Lines

Labels:
circle,
concurrent,
inscribed,
square

Subscribe to:
Post Comments (Atom)

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

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

Dear Peter problem 890 has more conclusions than problem 772

Deletehttp://img834.imageshack.us/img834/6712/8rc.png

ReplyDeleteSince 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

Let AE and CG intersect at a point Q, then we need to prove that Q,D,A,C,B concylic.

ReplyDelete∠QAD = ∠EAD = arctan(ED/AD) = arctan(DG/CD) = ∠GCD = ∠QCD

So Q,D,A,C concylic and the result follows.