megatron13 wrote:

XYZ is a right angled triangle with YZ = 6cm and XY = 8cm. XZ is the hypotenuse. A circle with center O and radius x has been inscribed in the triangle. What is the value of x?

A) 1.8

B) 2

C) 2.4

D) 3

E) 4

Draw the triangle, connect OX, OY, OZ

Hypotenuse = 10

Area of XYZ = 8*6/2 = 24

Area of OXZ = x*10/2 = 5x

Area of OXY = x*8/2 = 4x

Area of OYZ = x*6/2 = 3x

Area of OXZ + Area of OXY + Area of OYZ = Area of XYZ -> 5x + 4x + 3x = 24 ---> x = 2

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