Power of a point with respect to a circle

Question

I was reading the power of a circle from this-http://mathworld.wolfram.com/CirclePower.html Here they are saying tht the power of A with respect to the circle of radius r is given by $p= AP \times AQ$ but in the next case where they are calculating the power of P w.r.t. that circle they are writing $p=d^2-r^2$ (see at the link). But when I tried to calculate it myself I got $p=d(d-r)$ i.e. Power of P(according to the given definition) $p=PR\times PO =(OP-OR) \times OP =(d-r)d = d^2-rd$ I'm not getting the value which I should had.

Answer 1

O shouldn't be one of your two points. You need to compute $PR \cdot PS$, where $R$ and $S$ are the two points where $OP$ meets the circle. The segment $RS$ is a diameter.