Question

Two non intersecting circle of equal radii have their centre c1 and c2.If p lies on the perpendicular bisector of the line c1c2 show that the lengths of the tangents pl and pm form p to the circles are equal

Answer 1

Answer:

The radical axis of 2 circles is the locus of point from where length of tangent segments to both the circles is equal. Also, the radical axis is perpendicular to the line joining the centres of both the circles and its distance form the centre of C

1

is proportional to the radius of C

1

. Hence, if radical axis bisects the line joining centers of both the circles, they have equal radii.