Let r be the radius of the circle centered at O. If PD = 10 and PC = 15, and P is the midpoint of OB, what is r?
We can use the intersecting chord theorem here
Note that AO = r
And OP = (1/2)r
And PB = (1/2)r
So we have that
PD * PC = (AO + OP) (PB)
10 * 15 = [r + (1/2)r ] [ (1/2)r] simplify
150 = (3/2)r * (1/2)r
150 = (3/4)r^2 multiply both sides by 4/3
200 = r^2 take the positive root
√200 = r
10√2 = r