Question

Any two of three circles with centers A ,B and C touches each externally, If the lengths of AB, BC and CA be 5 cm, 6 cm and 7 cm respectively,then determine the radius of three circles ?

Answer 1

Let radius of circle with center A = R1
radius of circle with radius B = R2
radius of circle with radius C = R3

R1 + R2 = AB =  5 cm
R2 + R3 = BC = 6 cm
R3 + R1 = CA = 7 cm

add all three above equations and divide by 2,
R1 + R2 +R3 = 9 cm

Subtract the 1st equation from this equation,  R3 = 4 cm
solving,  R2 = 2 cm      and R1 = 3 cm