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3 points are collinear!

Source: IGO 2016,Advanced level,P1

September 13, 2016

geometrygeometry proposed

Problem Statement

Let the circles

\omega

and

\omega^ \prime

intersect in

A

and

B

. Tangent to circle

\omega

at

A

intersects

\omega^ \prime

in

C

and tangent to circle

\omega^ \prime

at

A

intersects

\omega

in

D

. Suppose that

CD

intersects

\omega

and

\omega^ \prime

in

E

and

F

, respectively (assume that

E

is between

F

and

C

). The perpendicular to

AC

from

E

intersects

\omega^ \prime

in point

P

and perpendicular to

AD

from

F

intersects

\omega

in point

Q

(The points

A, P

and

Q

lie on the same side of the line

CD

). Prove that the points

A, P

and

Q

are collinear. Proposed by Mahdi Etesami Fard

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