Question

With the vertices of $△$ABC as centers, three circles are described, each touching the other two externally. If the sides of the triangle are 7 cm, 8 cm and 11 cm, find the radii of the three circles.

Answer 1

Given that AB = 7 cm, BC = 8 cm, AC = 11cm.

Let AR = AP = x, BR = BQ =y, CQ = CP = z

x+y=7 …..(i)

y+z=8 => y=8-z

Substituting in (i)

x+8-z=7

x-z=-1 …..(ii)

Also x+z=11 …..(iii)

Adding (ii) and (iii)

2x=10 => x=5

Substituting in (i)

y=2

Substituting x=5 in (iii)

z=6

Therefore the radii of the 3 circles are 2 cm, 5 cm and 6 cm