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iran tst 2018 geometry

Source: Iranian TST 2018, second exam day 2, problem 5

April 17, 2018

geometry

Problem Statement

Let

\omega

be the circumcircle of isosceles triangle

ABC

(

AB=AC

). Points

P

and

Q

lie on

\omega

and

BC

respectively such that

AP=AQ

.

AP

and

BC

intersect at

R

. Prove that the tangents from

B

and

C

to the incircle of

\triangle AQR

(different from

BC

) are concurrent on

\omega

.
Proposed by Ali Zamani, Hooman Fattahi

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