Geometry Problem. Post your solution in the comments box below.

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

Click the figure below to view the complete problem 993

## Friday, March 14, 2014

### Geometry Problem 993: Intersecting Circles, Secant, Tangent, Concyclic Points, Cyclic Quadrilateral, Perpendicular

Labels:
circle,
concyclic,
cyclic quadrilateral,
perpendicular,
secant,
tangent

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<CBD=(<CBA=<ECD)+(<DBA=<EDC)=180-<CED, which makes CEDB cyclic and all points CEDBF lie on a circle. Then it is obvious that <FBE=<FDE=90.

ReplyDeleteIt also follows that <QFB=<DCB=<AOB/2=<QOB which makes points OQBF lie on a circle.