A CIRCLE IS TANGENT TO A LINE AT A. FROM A POINT P ON...

4. A circle is tangent to a line at A. From a point P on the circle, a line is drawn

such that PN is perpendicular to AN. If PN = 9 and AN = 15, determine the radius

of the circle.

P

A N

【Solution】

Let O be the center of the circle. Complete the

rectangle ANPQ. Let r be the radius of the circle.

Then

O

=

2

2

r OP

Q

= +

OQ QP

= − +

OA PN AN

( )

2

r

( 9) 225

This simplifies to 18r = 306 so that r = 17.

ANS: 17