In the figure given below AB = 7 cm BC = 8 cm CA = 5 cm. What are the radii of the circles A, B and C?
2 cm, 5 cm and 3 cm
AB is nothing but sum of radii of circle A and circle B. Likewise for BC and CA.
Let's try forming three simultaneous equations.
The radii of circles with centres A, B and C are x, y and z respectively.
x+y=7, y+z=8, z+x=5
⇒y=8−z, Putting this value in x+y=7
Solving for x, y and z, we get x = 2 cm, y = 5 cm and z = 3 cm