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

\(\therefore\) length of perpendicular to the line = radius.

\(\left|\frac{-b^2}{\sqrt{a^2}}\right| = c\)

b² = ac

\(\therefore\) a.b.c are in G.P.