MathDB

Let

P

be the intersection point of the diagonals of the quadrangle

ABCD

M

the intersection point of the lines connecting the midpoints of its opposite sides,

O

the intersection point of the perpendicular bisectors of the diagonals,

H

the intersection point of the lines connecting the orthocenters of the triangles

APD

and

BCP

APB

and

CPD

. Prove that

M

is the midpoint of

OH

Problem Statement