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 ?
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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
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
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