Question

Show that the area of the triangle formed by the two tangents from (x₁, y₁) to the circle x₂ + y² = a² and their chord of contact is

a(x²₁ + y₁² - a²)/^3/2/x₁² + y₁²

Answer 1

Let P = (x₁, y₁), O = (0, 0) and AB be the chord of contact (see Fig.). Suppose OP meets the chord AB at point M so that AM = MD and OM is perpendicular to AB. The equation of chord AB is given by

Now, the area of ΔPAB is given by