MathDB

Orthocenter, midpoints and angle bisectors

Source: Bosnia and Herzegovina Team Selection Test 2005 problem 1 day 1

October 6, 2017

geometryorthocenterangle bisectorcollinear

Problem Statement

Let

H

be an orthocenter of an acute triangle

ABC

. Prove that midpoints of

AB

and

CH

and intersection point of angle bisectors of

\angle CAH

and

\angle CBH

lie on the same line.