Equal tangents

In this problem students are given two circles with tangents that meet at a point P. The distance along the tangents from the circles to the point P are equal in length. The challenge is to describe the relationship between the x and y coordinates of the point P, given the coordinates of the centre of the circles and their radii.

In each student worksheet the circles have different centres and radii but the solutions have something in common.

To find the solution students must find the distance between points in the coordinate plane and use Pythagoras’ theorem. The solution requires students to combine the equations of the circles to form an equation giving the locus of point P.