Question

If the vertices of a triangle be (0, 0), (6, 0) and (6, 8), then its incentre will be ______.

पर्याय

• (2, 1)

• (1, 2)

• (4, 2)

• (2, 4)

Answer 1

If the vertices of a triangle be (0, 0), (6, 0) and (6, 8), then its incentre will be (4, 2).

Explanation:

Incentre = `((ax_1 + bx_2 + cx_3)/(a + b + c), (ay_1 + by_2 + cy_3)/(a + b + c))`

a = BC = `sqrt((8)^2` = 8

b = CA = `sqrt(36 + 64)` = 10

c = AB = `sqrt((6)^2)` = 6

∴ Incentre = `((8(0) + 10(6) + 6(6))/(8 + 10 + 6), (8(0) + 10(0) + 6(8))/(8 + 10 + 6))`

= `((0 + 60 + 36)/2, (0 + 0 + 48)/24)`

= `(96/24, 48/24)`

= (4, 2)