MathDB

Right angle [Switzerland 2011]

Source:

January 31, 2011

geometrygeometric transformationreflectiongeometry proposed

Problem Statement

Let

ABCD

an inscribed quadrilateral and

r

and

s

the reflections of the straight line through

A

and

B

over the inner angle bisectors of angles

\angle{CAD}

and

\angle{CBD}

, respectively. Let

P

the point of intersection of

r

and

s

and let

O

the circumcentre of

ABCD

. Prove that

OP \perp CD