MathDB

Let

ABC

be a triangle contained in one of the halfplanes determined by a line

r

. Points

A',B',C'

are the reflections of

A,B,C

r,

respectively. Consider the line through

A'

parallel to

BC

, the line through

B'

parallel to

AC

and the line through

C'

parallel to

AB

. Show that these three lines have a common point.

Problem Statement