MathDB

Consider an acute triangle

ABC

and its altitudes from

A

B

that intersect the respective sides at

D ,E

. Let us call the point of intersection of the altitudes

H

. Construct the circle with center

H

and radius

HE

. From

C

draw a tangent line to the circle at point

P

. With center

B

and radius

BE

draw another circle and from

C

another tangent line is drawn to this circle in the point

Q

. Prove that the points

D, P

, and

Q

are collinear.

Problem Statement