Geometry Problem

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

Click the figure below to see the complete problem 916.

## Wednesday, September 4, 2013

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

Labels:
circle,
congruence,
cyclic quadrilateral,
diameter

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draw DF,EA,AC and BD

ReplyDeleteAEB=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

http://img62.imageshack.us/img62/4753/c84r.png

ReplyDeleteConnect 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