MathDB

P12

Part of 2017 Sharygin Geometry Olympiad

Problems(1)

Symmedian passes through intersection of two circumcircle

Source: Sharygin Geometry Olympiad Correspondence Round 2017 P-12 (Grade-9-10)

5/1/2017
Let AA1,CC1AA_1 , CC_1 be the altitudes of triangle ABC,B0ABC, B_0 the common point of the altitude from BB and the circumcircle of ABCABC; and QQ the common point of the circumcircles of ABCABC and A1C1B0A_1C_1B_0, distinct from B0B_0. Prove that BQBQ is the symmedian of ABCABC. Proposed by D.Shvetsov
geometrycircumcircle