MathDB

|SA'| |SB'| = |SN|^2

Source: Baltic Way 1994

December 22, 2011

geometry proposedgeometry

Problem Statement

Let

NS

and

EW

be two perpendicular diameters of a circle

\mathcal{C}

. A line

\ell

touches

\mathcal{C}

at point

S

. Let

A

and

B

be two points on

\mathcal{C}

, symmetric with respect to the diameter

EW

. Denote the intersection points of

\ell

with the lines

NA

and

NB

by

A'

and

B'

, respectively. Show that

|SA'|\cdot |SB'|=|SN|^2

.

Back to Problems View on AoPS