MathDB

2007 Guts #18: Diagonals of Convex Quadrilateral

Source:

June 22, 2012

geometrycircumcircle

Problem Statement

Convex quadrilateral

ABCD

has right angles

\angle A

and

\angle C

and is such that

AB=BC

and

AD=CD

. The diagonals

AC

and

BD

intersect at point

M

. Points

P

and

Q

lie on the circumcircle of triangle

AMB

and segment

CD

, respectively, such that points

P

,

M

, and

Q

are collinear. Suppose that

m\angle ABC=160^\circ

and

m\angle QMC=40^\circ

. Find

MP\cdot MQ

, given that

MC=6

.

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