MathDB

ABCD

is convex

AD\parallel BC

AC\perp BD

M

is interior point of

ABCD

which is not a intersection of diagonals

AC

and

BD

such that \angle AMB \equal{}\angle CMD \equal{}\frac{\pi}{2} .

P

is intersection of angel bisectors of

\angle A

and

\angle C

Q

is intersection of angel bisectors of

\angle B

and

\angle D

. Prove that \angle PMB \equal{}\angle QMC.

Problem Statement