MathDB

17

Part of 2009 Sharygin Geometry Olympiad

Problems(1)

a concurrency problem

Source: I.F.Sharygin contest 2009 - Correspondence round - Problem 17

5/31/2009
Given triangle ABC ABC and two points X X, Y Y not lying on its circumcircle. Let A1 A_1, B1 B_1, C1 C_1 be the projections of X X to BC BC, CA CA, AB AB, and A2 A_2, B2 B_2, C2 C_2 be the projections of Y Y. Prove that the perpendiculars from A1 A_1, B1 B_1, C1 C_1 to B2C2 B_2C_2, C2A2 C_2A_2, A2B2 A_2B_2, respectively, concur if and only if line XY XY passes through the circumcenter of ABC ABC.
geometrycircumcircleratiogeometry proposed