MathDB

Cyclic quadrilateral and reflections wrt bisectors

Source: Brazilian Math Olympiad 2008, Problem 4

October 28, 2008

geometrygeometric transformationreflectioncircumcircleincenterhomothetycyclic quadrilateral

Problem Statement

Let

ABCD

be a cyclic quadrilateral and

r

and

s

the lines obtained reflecting

AB

with respect to the internal bisectors of

\angle CAD

and

\angle CBD

, respectively. If

P

is the intersection of

r

and

s

and

O

is the center of the circumscribed circle of

ABCD

, prove that

OP

is perpendicular to

CD