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JEE Main20262 April 2026Morning ShiftMathematicsStraight LinesActual

Let the mid points of the sides of a triangle ABC be ( 5 2 , 7 ) , ( 5 2 , 3 ) and (4, 5) . If its incentre is (h, k) , then 3h + k is equal to :

Options

  1. A11
  2. B12
  3. C13
  4. D14

Correct answer

C. 13

Step-by-step solution

Let the vertices of the triangle ABC be A(x₁, y₁) , B(x₂, y₂) , and C(x₃, y₃) . Let the given midpoints be of sides BC , CA , and AB respectively: Midpoint of BC = ( 5 2 , 7 ) x₂ + x₃ = 5 and y₂ + y₃ = 14 Midpoint of CA = ( 5 2 , 3 ) x₃ + x₁ = 5 and y₃ + y₁ = 6 Midpoint of AB = (4, 5) x₁ + x₂ = 8 and y₁ + y₂ = 10 Adding the three equations for the x -coordinates: 2(x₁ + x₂ + x₃) = 5 + 5 + 8 = 18 x₁ + x₂ + x₃ = 9 Substituting the known sums: x₁ = 9 - 5 = 4 x₂ = 9 - 5 = 4 x₃ = 9 - 8 = 1 Similarly, for y -coordinates:

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