*arbitrary line*passing though $P$.

Power of a point: ${\cal P}(P, (O)) = \vec{PU} \times \vec{PV} = PO^2 - r^2 = (P_x - O_x)^2 + (P_y - O_y)^2 - r^2$. |

The value of the power of a point gives us information about relative position of the point with respect to the circle. If the power of the point $P$ is a

*positive*number then $P$ is

*outside*the circle, if it is a

*negative*number then $P$ is

*inside*the circle, and if it is equal to

*zero*then $P$ is

*on the circle*.

Today, we will look at application of the power of a point concept. We will use two main tools:

**radical axis**and**radical center**. Radical axis is often used to prove that a certain number of points lie on the same straight line, and radical center is used to prove a certain number of lines meet at a common point.