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I, Blaise Pascal, have a dream

Source: Sharygin Correspondence Round 2024 P21

March 6, 2024

geometrycircumcircle

Problem Statement

A chord

PQ

of the circumcircle of a triangle

ABC

meets the sides

BC, AC

at points

A', B'

respectively. The tangents to the circumcircle at

A

and

B

meet at a point

X

, and the tangents at points

P

and

Q

meet at point

Y

. The line

XY

meets

AB

at a point

C'

. Prove that the lines

AA', BB'

and

CC'

concur.

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