MathDB

rectangle wanted, starting with a cyclic ABCD and angle bisectors

Source: 2012 Balkan Shortlist G7 BMO

April 3, 2020

geometryrectangleangle bisectorcyclic quadrilateralCyclic

Problem Statement

ABCD

is a cyclic quadrilateral. The lines

AD

and

BC

meet at X, and the lines

AB

and

CD

meet at

Y

. The line joining the midpoints

M

and

N

of the diagonals

AC

and

BD

, respectively, meets the internal bisector of angle

AXB

P

and the external bisector of angle

BYC

Q

. Prove that

PXQY

is a rectangle