# Math Help - radius of circle

A point P is outside a circle and is 13 inches from the center. A secant from P cuts the circle at Q and R so that the external segment of the secant PQ is 9 inches and QR is 7 inches. The radius of the circle is :

I don't get the problem.

2. Originally Posted by Veronica1999
A point P is outside a circle and is 13 inches from the center. A secant from P cuts the circle at Q and R so that the external segment of the secant PQ is 9 inches and QR is 7 inches. The radius of the circle is :

I don't get the problem.
1. Draw a sketch.

2. You are dealing with 2 right triangles. Use the Pythagorian theorem:

$\left|\begin{array}{rcl}r^2&=&(3.5)^2+h^2 \\ h^2 +(3.5+9)^2&=&13^2\end{array}\right.$

Solve for h and r.

3. Originally Posted by earboth
1. Draw a sketch.

2. You are dealing with 2 right triangles. Use the Pythagorian theorem:

$\left|\begin{array}{rcl}r^2&=&(3.5)^2+h^2 \\ h^2 +(3.5+9)^2&=&13^2\end{array}\right.$

Solve for h and r.

You are awesome!!!!!
Thanks.

4. Hi Ronsy,

After studying Earboth's sketch for a while, I realized there is another way to solve it. You can use the rates of the sides.

16/13+r = 13-r/9

Vicky.