MathDB

three circles

Source: Mexico 2003

March 2, 2007

geometryparallelogrampower of a pointradical axisgeometry unsolved

Problem Statement

A, B, C

are collinear with

B

betweeen

A

and

C

.

K_{1}

is the circle with diameter

AB

, and

K_{2}

is the circle with diameter

BC

. Another circle touches

AC

at

K_{1}

and meets

K_{1}

again at

K_{2}

and

K_{2}

again at

AR

. The line

PQ

meets

K_{1}

again at

R

and

K_{2}

again at

S

. Show that the lines

AR

and

CS

meet on the perpendicular to

AC

at

B

.

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