MathDB

11

Part of 2012 Sharygin Geometry Olympiad

Problems(1)

Concurrent lines

Source: Sharygin Geometry Olympiad 2012 - Problem 11

4/28/2012
Given triangle ABCABC and point PP. Points A′,B′,C′A', B', C' are the projections of PP to BC,CA,ABBC, CA, AB. A line passing through PP and parallel to ABAB meets the circumcircle of triangle PA′B′PA'B' for the second time in point C1C_{1}. Points A1,B1A_{1}, B_{1} are defined similarly. Prove that a) lines AA1,BB1,CC1AA_{1}, BB_{1}, CC_{1} concur; b) triangles ABCABC and A1B1C1A_{1}B_{1}C_{1} are similar.
geometrycircumcirclegeometry unsolved