MathDB

Let

ABC

be a right triangle, with the right angle at

A

. The altitude from

A

meets

BC

H

and

M

is the midpoint of the hypotenuse

[BC]

. On the legs, in the exterior of the triangle, equilateral triangles

BAP

and

ACQ

are constructed. If

N

is the intersection point of the lines

AM

and

PQ

, prove that the angles

\angle NHP

and

\angle AHQ

are equal.
Miguel Ochoa Sanchez and Leonard Giugiuc

Problem Statement