MathDB
Intersection satisfying a symmetric condition

Source: 2017 Korea Winter Program Practice Test 1 Day 2 #3

January 21, 2017
geometryTST

Problem Statement

Let △ABC\triangle ABC be a triangle with ∠A≠60∘\angle A \neq 60^\circ. Let IB,ICI_B, I_C be the B,CB, C-excenters of triangle ABCABC, let B′B^\prime be the reflection of BB with respect to ACAC, and let C′C^\prime be the reflection of CC with respect to ABAB. Let PP be the intersection of ICB′I_C B^\prime and IBC′I_B C^\prime. Denote by PA,PB,PCP_A, P_B, P_C the reflections of the point PP with respect to BC,CA,ABBC, CA, AB. Show that the three lines APA,BPB,CPCA P_A, B P_B, C P_C meet at a single point.
Back to ProblemsView on AoPS