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Let the incentre of Δ A B C is I 2 , 5 . If A = 1 , 13 and B = - 4 , 1 , then the sum of the slopes of sides A C and B C is

Options

  1. A3 4
  2. B- 4 3
  3. C4 3
  4. D- 3 4

Correct answer

B. - 4 3

Step-by-step solution

Slope of A B is 13 - 1 1 - - 4 = 12 5 Slope of BI is 5 - 1 2 - - 4 = 2 3 Slope of A I is 13 - 5 1 - 2 = - 8 Let, the slopes of B C and A C are m 1 and m 2 respectively tan ⁡ A 2 = tan ⁡ A 2 ⇒ m 2 - - 8 1 + m 2 - 8 = - 8 - 12 5 1 + - 8 12 5 m 2 + 8 91 = 1 - 8 m 2 52 ⇒ m 2 = - 4 3 Now tan ⁡ B 2 = tan ⁡ B 2 ⇒ m 1 - 2 3 1 + m 1 2 3 = 2 3 - 12 5 1 + 2 3 × 12 5 ⇒ 3 m 1 - 2 39 = 3 + 2 m 1 - 26 ⇒ m 1 = 0 ⇒ m 1 + m 2 = - 4 3

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