MathDB

1

Part of 2005 Bosnia and Herzegovina Team Selection Test

Problems(1)

Orthocenter, midpoints and angle bisectors

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

10/6/2017
Let HH be an orthocenter of an acute triangle ABCABC. Prove that midpoints of ABAB and CHCH and intersection point of angle bisectors of ∠CAH\angle CAH and ∠CBH\angle CBH lie on the same line.
geometryorthocenterangle bisectorcollinear