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St. Petersburg MO 2017 Grade 11 P2

Source: St. Petersburg MO 2017 Grade 11 P2

May 3, 2018

geometry

Problem Statement

A circle passing through vertices

A

and

B

of triangle

ABC

intersects the sides

AC

and

BC

again at points

P

and

Q

, respectively. Given that the median from vertex

C

bisect the arc

PQ

of the circle. Prove that

ABC

is an isosceles triangle.

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