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China Mathematics Olympiads (National Round) 2010 Problem 1

Source:

November 28, 2010

geometryincenterChina

Problem Statement

Two circles

\Gamma_1

and

\Gamma_2

meet at

A

and

B

. A line through

B

meets

\Gamma_1

and

\Gamma_2

again at

C

and

D

repsectively. Another line through

B

meets

\Gamma_1

and

\Gamma_2

again at

E

and

F

repsectively. Line

CF

meets

\Gamma_1

and

\Gamma_2

again at

P

and

Q

respectively.

M

and

N

are midpoints of arc

PB

and arc

QB

repsectively. Show that if

CD = EF

, then

C,F,M,N

are concyclic.

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