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Cyclic quadrilateral geo

Source: Russian TST 2014, Day 10 P2 (Groups A & B)

January 8, 2024

geometrycyclic quadrilateral

Problem Statement

In the quadrilateral

ABCD

the angles

B{}

and

D{}

are straight. The lines

AB{}

and

DC{}

intersect at

E

and the lines

AD

and

BC

intersect at

F{}.

The line passing through

B{}

parallel to

C{}

D intersects the circumscribed circle

\omega

of

ABF{}

at

K{}

and the segment

KE{}

intersects

\omega

at

P{}.

Prove that the line

AP

divides the segment

CE

in half.

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