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JEE Main20199 Jan 2019Morning ShiftMathematicsCircleActual

Three circles of radii a , b , c , a < b < c touch each other externally. If they have x - axis as a common tangent, then:

Options

  1. A1 a = 1 b + 1 c
  2. Ba , b , c are in A.P.
  3. C1 b = 1 a + 1 c
  4. Da , b , c are in A.P.

Correct answer

A. 1 a = 1 b + 1 c

Step-by-step solution

We have, L M = P N = a + b 2 - b - a 2 = 2 a b N Q = M S = a + c 2 - c - a 2 = 2 a c P Q = S T = b + c 2 - c - b 2 = 2 b c ∵ P Q = P N + N Q ⇒ 2 b c = 2 a b + 2 a c ⇒ 1 a = 1 b + 1 c

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