## Radical Axis

#### Problem

Two circles, centred at A and B, intersect at X and Y. From a point, P, on the common secant through XY, tangents are drawn to each circle at S and T.

The locus of points, P, for which PT = PS is called the radical axis.

Prove that the common secant is the radical axis.

Problem ID: 194 (21 Dec 2004) Difficulty: 3 Star