Question

ABC is a triangle with AB = 10 cm, BC = 8 cm and AC = 6 cm (not drawn to scale). Three circle are drawn touching each other with the vertices as their centres. Find the radii of the three circles.

Answer 1

Given: ABC is a triangle with AB = 10 cm, BC = 8 cm, AC = 6 cm. Three circles are drawn with centre A, B and C touch each other at P, Q and R respectively.

We need to find the radii of the three circles.

Let

PA = AQ = x

QC = CR = y

RB = BP = z

∴ x + z = 10  ...(1)

z + y = 8   ...(2)

y + x = 6  ...(3)

Adding all the three equations, we have

2(x + y + z) = 24

`=> x + y + z = 24/2 = 12`   ...(4)

Subtracting (1) (2) and (3) from (4)

y = 12 – 10 = 2

x = 12 – 8 = 4                                                           

z = 12 – 6 = 6

Therefore, radii are 2 cm, 4 cm and 6 cm