# Math Help - Finding the radius of a circle.

1. ## Finding the radius of a circle.

I'm stuck with this question: I am given a circle, and I have to find the radius.

Given: Line AC is a tangent to the circle, and line EH is paralell to it. The length of FB is 10, and the length of FG is 12. EH does not pass through the center.

From this, I got that the line BD is equal to 8, and if you were to draw point z at the bottom of the circle, directly opposite to point A, angle AFZ and AGZ would equal to 90 degrees each. I'm stuck. Help is greatly appreciated.

Thank you so much!

2. Let O be the center.

$OD=R-8$

In the triangle ODF apply Pitagora:

$R^2=6^2+(R-8)^2$

Now solve the equation.