# Math Help - Find a Radius

A circle has a chord, AB, of 20cm. Point C is on AB, 8cm from A (and 12cm from B. I'm not entirely hopeless!) Point D is on the circle, 6cm from point C, and CD is perpendicular to AB.

-What is the radius of the circle?
-How far is point C from the center?

2. Originally Posted by English Major
A circle has a chord, AB, of 20cm. Point C is on AB, 8cm from A (and 12cm from B. I'm not entirely hopeless!) Point D is on the circle, 6cm from point C, and CD is perpendicular to AB.

-What is the radius of the circle?
-How far is point C from the center?
1. Draw a sketch (see attachment)

2. F is the midpoint of AB. Then the center of the circle is placed on a line through F perpendicular to AB.

3. The distance of the center of the circle to AB is called x.

4. You get 2 right triangles with the radius as hypotenuse. (Note that CF = 2) Use Pythagorean theorem:

$(6+x)^2 + 2^2 = r^2$ ........ [1]

$x^2 + 10^2 = r^2$ ........ [2]

5. Solve for x:

$(6+x)^2 + 2^2 = x^2 + 10^2$ ........ I've got x = 5

6. Thus $r = 5\cdot \sqrt{5}$

7. I'll leave the rest for you.