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Turkey NMO 2010 P4

Source:

December 15, 2010

geometrycircumcirclegeometry proposed

Problem Statement

Let

A

and

B

be two points on the circle with diameter

[CD]

and on the different sides of the line

CD.

A circle

\Gamma

passing through

C

and

D

intersects

[AC]

different from the endpoints at

E

and intersects

BC

at

F.

The line tangent to

\Gamma

at

E

intersects

BC

at

P

and

Q

is a point on the circumcircle of the triangle

CEP

different from

[EQ].

and satisfying

|QP|=|EP|. \: AB \cap EF =\{R\}

and

S

is the midpoint of

[EQ].

Prove that

DR

is parallel to

PS.

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