MathDB

Radical axis perpendicular to MK

Source: Iran 1996 Third Round

June 7, 2010

geometrycircumcircleEulercyclic quadrilateralpower of a pointradical axis

Problem Statement

Consider a semicircle of center

O

and diameter

AB

. A line intersects

AB

M

and the semicircle at

C

and

D

s.t.

MC>MD

and

MB<MA

. The circumcircles od the

AOC

and

BOD

intersect again at

K

. Prove that

MK\perp KO