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Two tangents AT and BT touch a circle at A and B

Source: Canadian Repêchage 2010: Problem 2

May 6, 2014

geometryrectanglegeometry proposed

Problem Statement

Two tangents

AT

and

BT

touch a circle at

QRST

and

B

, respectively, and meet perpendicularly at

T

.

Q

is on

AT

,

S

is on

BT

, and

R

is on the circle, so that

QRST

is a rectangle with

QT = 8

and

ST = 9

. Determine the radius of the circle.

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