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Concurrent lines

Source: Sharygin Geometry Olympiad 2012 - Problem 11

April 28, 2012

geometrycircumcirclegeometry unsolved

Problem Statement

Given triangle

BC, CA, AB

and point

P

. Points

A', B', C'

are the projections of

P

to

BC, CA, AB

. A line passing through

P

and parallel to

AB

meets the circumcircle of triangle

PA'B'

for the second time in point

C_{1}

. Points

A_{1}, B_{1}

are defined similarly. Prove that a) lines

AA_{1}, BB_{1}, CC_{1}

concur; b) triangles

ABC

and

A_{1}B_{1}C_{1}

are similar.

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