MathDB

20

Part of 2009 Sharygin Geometry Olympiad

Problems(1)

nice concyclic

Source: I.F.Sharygin contest 2009 - Correspondence round - Problem 20

5/31/2009
Suppose H H and O O are the orthocenter and the circumcenter of acute triangle ABC ABC; AA1 AA_1, BB1 BB_1 and CC1 CC_1 are the altitudes of the triangle. Point C2 C_2 is the reflection of C C in A1B1 A_1B_1. Prove that H H, O O, C1 C_1 and C2 C_2 are concyclic.
geometrycircumcirclegeometric transformationreflectiontrigonometrygeometry proposed