MathDB

3 parallel lines, symmetric points wrt angle bisectors

Source: Netherlands - Dutch NMO 1979 p4

January 28, 2023

geometryparallelsymmetryangle bisector

Problem Statement

Given is the non-equilateral triangle

A_1A_2A_3

B_{ij}

is the symmetric of

A_i

wrt the inner bisector of

\angle A_j

. Prove that lines

B_{12}B_{21}

B_{13}B_{31}

and

B_{23}B_{32}

are parallel.