MathDB

P16

Part of 2016 Sharygin Geometry Olympiad

Problems(1)

common point of circles lies on Euler line

Source: Sharygin Geometry Olympiad 2016 First Round P16 grades 9-11

7/25/2018
Let BB1BB_1 and CC1CC_1 be altitudes of triangle ABCABC. The tangents to the circumcircle of AB1C1AB_1C_1 at B1B_1 and C1C_1 meet AB and ACAC at points MM and NN respectively. Prove that the common point of circles AMNAMN and AB1C1AB_1C_1 distinct from AA lies on the Euler line of ABCABC.
geometrycircumcircleEuler Line