MathDB

Symmedians of ABC and ABH intersect on line between feet of altitudes

Source: Germany 2023, Problem 5

June 16, 2023

geometrygeometry proposedsymmedianIntersection

Problem Statement

Let

ABC

be an acute triangle with altitudes

AA'

and

BB'

and orthocenter

H

. Let

C_0

be the midpoint of the segment

AB

. Let

g

be the line symmetric to the line

CC_0

with respect to the angular bisector of

\angle ACB

. Let

h

be the line symmetric to the line

HC_0

with respect to the angular bisector of

\angle AHB

.
Show that the lines

g

and

h

intersect on the line

A'B'