MathDB

Let

ABCD

be a quadrilateral that can be inscribed in a circle whose diagonals are perpendicular. Denote by

P

and

Q

the feet of the perpendiculars through

D

and

C

respectively on the line

AB

X

is the intersection point of the lines

AC

and

DP

Y

is the intersection point of the lines

BD

and

CQ

. Show that

XY CD

is a square.

Problem Statement