MathDB

16

Part of 2011 Sharygin Geometry Olympiad

Problems(1)

concurrent lines related to reflections of a line wrt to sides of given triangle

Source: 2011 Sharygin Geometry Olympiad Correspondence Round P16

4/6/2019
Given are triangle ABCABC and line ℓ\ell. The reflections of ℓ\ell in ABAB and ACAC meet at point A1A_1. Points B1,C1B_1, C_1 are defined similarly. Prove that a) lines AA1,BB1,CC1AA_1, BB_1, CC_1 concur, b) their common point lies on the circumcircle of ABCABC c) two points constructed in this way for two perpendicular lines are opposite.
geometryreflectionconcurrencyconcurrentReflections