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 9 cm, 7 cm and 6 cm, find the radii of the circles. [4 MARKS]

Answer 1

Concept: 1 Mark
Application: 3 Marks

Let AB = 9 cm, BC = 7 cm and CA = 6 cm.

Let x, y, z be the radii of circles with centers A, B, C respectively.

Then, x + y = 9, y + z = 7 and z + x = 6

Adding, we get $2(x+y+z)=22\Rightarrow x+y+z=11$.

Therefore, x = [(x + y + z) – (y + z)] = (11 – 7) cm = 4 cm.

Similarly, y = (11 – 6) cm = 5 cm and z = (11 – 9) cm = 2 cm.

Hence, the radii of circles with centers A, B, C are 4 cm, 5cm and 2 cm respectively.