Let ABC be an acute triangle such that AB is the shortest side of the triangle. Let D be the midpoint of the side AB and P be an interior point of the triangle such that ∠CAP=∠CBP=∠ACB. Denote by M and N the feet of the perpendiculars from P to BC and AC, respectively. Let p be the line through M parallel to AC and q be the line through N parallel to BC. If p and q intersect at K prove that D is the circumcenter of triangle MNK. geometryCircumcenterequal anglescircumcircle