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Let circles C 1 , C 2 and C 3 with centres O 1 , O 2 and O 3 respectively touch each other externally, where O 1 = - 36,7 , O 2 = 20,7 and O 3 = 0 , - 8 . The coordinates of the centre of a circle passing through the points of contact of circles C 1 , C 2 and C 2 , C 3 and C 3 , C 1 are

Options

  1. A- 1,0
  2. B1,0
  3. C0,1
  4. D0 , - 1

Correct answer

A. - 1,0

Step-by-step solution

The circle which passes through the points of contact of circles C 1 , C 2   &   C 2 , C 3   &   C 3 , C 1 is the incircle of Δ O 1 O 2 O 3 . Its centre lies on the angle bisectors of Δ O 1 O 2 O 3 . Hence, required point is incentre of Δ O 1 O 2 O 3 . Now, O 1 O 2 = 56 ,   O 2 O 3 = 25   &   O 3 O 1 = 39 ⇒ Ι = 56 × 0 + 25 × - 36 + 39 × 20 56 + 25 + 39 , 25 × 7 + 56 × - 8 + 39 7 25 + 56 + 39 = - 1,0

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