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Tangent intersect intersect tangent intersect

Source: Iranian Geometry Olympiad 2016 Medium 2

May 26, 2017

geometry

Problem Statement

Let two circles

C_1

and

C_2

intersect in points

A

and

B

. The tangent to

C_1

at

A

intersects

C_2

in

P

and the line

PB

intersects

C_1

for the second time in

Q

(suppose that

Q

is outside

C_2

). The tangent to

C_2

from

Q

intersects

C_1

and

C_2

in

C

and

D

, respectively. (The points

A

and

D

lie on different sides of the line

PQ

.) Show that

AD

is the bisector of

\angle CAP

.
Proposed by Iman Maghsoudi

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