MathDB

Let

H

and

I

be the orthocenter and incenter, respectively, of an acute-angled triangle

ABC

. The circumcircle of the triangle

BCI

intersects the segment

AB

at the point

P

different from

B

. Let

K

be the projection of

H

onto

AI

and

Q

the reflection of

P

K

. Show that

B

H

and

Q

are collinear.
Proposed by Mads Christensen, Denmark

Problem Statement