Find incentre of the triangle With vertices A(1,2) B(1,4) C(3,4)

The vertices of the triangle are A (1,2) ,B (1,4) and C (3,4)

a = BC = √(1-3)² + (4-4)²

          =  2

b = CA = √(3-1)² + (4-2)²

          =  √(2)² + (2)²

          =  2√2     

c = AB = √(1-1)² + (2-4)²

          =  2

Incentre I of the triangle is

[(ax₁ + bx₂ + cx₃)/(a+b+c),(ay₁ + by₂ + cy₃)/(a+b+c)]

      x₁ = 1 y₁ = 2 x₂ = 1 y₂ = 4  x₃ = 3 y₃ = 4

       a = 2 b = 2√2  c = 2

= [2(1) + 2√2(1) + 2(3)/(2 + 2√2 + 2),2(2) + 2√2(4) + 2(4)/(2 + 2√2 + 2)  

= [(8+2√2)/(4+2√2),(12+8√2)/(4+2√2)]

Hope it clears........................