MathDB

Concurrency

Source: China TST 2006

June 18, 2006

geometrycircumcirclegeometric transformationreflectionprojective geometrypower of a pointradical axis

Problem Statement

The centre of the circumcircle of quadrilateral

ABCD

O

and

O

is not on any of the sides of

ABCD

P=AC \cap BD

. The circumecentres of

\triangle{OAB}

\triangle{OBC}

\triangle{OCD}

and

\triangle{ODA}

are

O_1

O_2

O_3

and

O_4

respectively. Prove that

O_1O_3

O_2O_4

and

OP

are concurrent.