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Prove that BFO is right if AEDC is cyclic

Source: All-Russian MO 1999

December 31, 2012

radical axisgeometry

Problem Statement

A circle through vertices

A

and

B

of triangle

ABC

meets side

BC

again at

D

. A circle through

C

and

O

meets side

\angle BFO

at

E

and the first circle again at

F

. Prove that if points

A

,

E

,

D

,

C

lie on a circle with center

O

then

\angle BFO

is right.

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