MathDB

Consider a rhombus

ABCD

with center

O

. A point

P

is given inside the rhombus, but not situated on the diagonals. Let

M,N,Q,R

be the projections of

P

on the sides

(AB), (BC), (CD), (DA)

, respectively. The perpendicular bisectors of the segments

MN

and

RQ

meet at

S

and the perpendicular bisectors of the segments

NQ

and

MR

meet at

T

. Prove that

P, S, T

and

O

are the vertices of a rectangle.

Problem Statement