Probability and Area calculation

I'm not sure of what is the correct section to post this, anyway...

Consider this:

http://e.nigma.be/wp-content/uploads.../racchetta.png

The only given data is **f**, **R**, **t**, **r** and **g**.

if the center of the ball (the orange one) is inside the circle of radius R what is the probability of the ball to do not pass through a white area?

I wrote a better explanation here using bold,italic,images ect and I don't think it's necessary to paste it here...

I tried to solve it (It's not the programming part of the problem my problem, but the math part...) but I got wrong result. I'd like to understand why my solution is wrong, I tried to do it without integrals.

Thank you