Question

The chord of contact of tangents drawn from a point on the circle x² + y² = a² to the circle x² + y² = b² touches the circle x² + y² = c² show that a.b.c are in GP. 

Answer 1

Let P (a cosθ ,asinθ) be a point on the circle x² + y² = a² Then equation of chord of contact to the circle x² + y² = b² from P (a cosθ , asinθ) is

x(a cosθ) + y (asinθ) = b² 

axcosθ + aysinθ = b²

It is a tangent to the circle x² + y² =  c² 

length of perpendicular to the line = radius.

b² = ac

a, b.c are in G.P.