MathDB

Geometry Problem (15)

Source:

August 7, 2010

geometrycircumcirclecyclic quadrilateralgeometric transformationgeometry proposedSpiral SimilarityRussian

Problem Statement

The diagonals of a cyclic quadrilateral

ABCD

meet at

O

. Let

S_1, S_2

be the circumcircles of triangles

ABO

and

CDO

respectively, and

O,K

their intersection points. The lines through

O

parallel to

AB

and

CD

meet

S_1

and

S_2

again at

L

and

M

, respectively. Points

P

and

Q

on segments

OL

and

OM

respectively are taken such that

OP : PL = MQ : QO

. Prove that

O,K, P,Q

lie on a circle.

Back to Problems View on AoPS