Circle geometry: what is the distance between $OA$?

Question

Having the following image, and assuming $AQ$ and $AP = 9$cm, and the diameter of the circle is $30$ cm, what is the distance between $OA$?

I have tried almost everything including trig, but it doesn't work out, and makes no sense to me, so please help!!!

Answer 1

Root of 306 (pythagorean theorem)

Answer 2

Tangent is perpendicular to the radius. Hence, $AO^2 = OQ^2 + AQ^2$. Note that $AQ=9$, $OQ=15$, so $OA = \sqrt{81+225} = \sqrt{306}$.