If the chord of contact of the tangents from the point α , β to the circle x 2 + y 2 = r 1 2 is a tangent to the circle x - a 2 + y - b 2 = r 2 2 , then

Question

If the chord of contact of the tangents from the point α , β to the circle x 2 + y 2 = r 1 2 is a tangent to the circle x - a 2 + y - b 2 = r 2 2 , then, r 2 2 α 2 + β 2 = r 1 2 - a α - b β 2, r 2 2 α 2 + β 2 = r 1 2 + a α - b β 2, r 2 2 α 2 + β 2 = r 1 2 - a α + b β 2, r 2 2 α 2 + β 2 = r 1 2 + a α + b β 2

MARKS App · Accepted Answer

The equation of the chord of contact of tangents drawn from a point α , β to the circle x 2 + y 2 = r 1 2 is α x + β y = r 1 2 This line touches the circle x - a 2 + y - b 2 = r 2 2 ∴ a α + b β - r 1 2 α 2 + β 2 = r 2 ⇒ r 2 2 α 2 + β 2 = a α + b β - r 1 2 2 ⇒ r 2 2 α 2 + β 2 = r 1 2 - a α - b β 2

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