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$R, B$ and $R'$ are collinear

Source: 39-th Vietnamese Mathematical Olympiad 2001

March 19, 2007

ratiogeometrypower of a pointradical axisperpendicular bisectorgeometry unsolved

Problem Statement

A circle center

O

meets a circle center

O'

A

and

B.

The line

TT'

touches the first circle at

T

and the second at

T'

. The perpendiculars from

T

and

T'

meet the line

OO'

S

and

S'

. The ray

AS

meets the first circle again at

R

, and the ray

AS'

meets the second circle again at

R'

. Show that

R, B

and

R'

are collinear.