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If the lengths of the tangents from P 1,3 and Q 3,7 to a circle are 2 units and 18 units respectively, then the length of the tangent from R 7,15 to the same circle is

Options

  1. A98 units
  2. B170 units
  3. C50 units
  4. DNone of these

Correct answer

B. 170 units

Step-by-step solution

Let, circle is x 2 + y 2 + 2 g x + 2 f y + C = 0 and the length of the tangent from 7 , 15 as l units, then 1 + 9 + 2 g + 6 f + C = 2 … 1 9 + 49 + 6 g + 14 f + C = 18 … 2 49 + 225 + 14 g + 30 f + C = l 2 … 3 Now, equation 2 1 + 3 implies 2 + 18 + 49 + 225 + 18 g + 42 f + 3 C = 4 + l 2 ⇒ 69 + 225 + 3 6 g + 14 f + C = 4 + l 2 ⇒ 69 + 225 + 3 18 - 58 = 4 + l 2 (from 2 ) ⇒ l 2 = 225 + 69 - 4 - 12 0 ⇒ l 2 = 170 ⇒ l = 170 ⇒ length of the tangent from R is 170 units

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