MathDB

In an acute-angled triangle

ABC

, we consider the feet

H_a

and

H_b

of the altitudes from

A

and

B

, and the intersections

W_a

and

W_b

of the angle bisectors from

A

and

B

with the opposite sides

BC

and

CA

respectively. Show that the centre of the incircle

I

of triangle

ABC

lies on the segment

H_aH_b

if and only if the centre of the circumcircle

O

of triangle

ABC

lies on the segment

W_aW_b

Problem Statement