Question

Two circles with centres A and B are touching externally. A circle with centre C touches both
the circles externally. Suppose AB = 3 cm, BC = 3 cm and CA = 4 cm. Find the radii of the
circles.​

Answer 1

Radius of circles = 2 , 1 , 2 cm

Step-by-step explanation:

AB  = 3 cm

BC = 3 cm

CA = 4 cm

AB = R₁ + R₂  = 3 cm

BC = R₂ + R₃ = 3  cm

CA = R₁ + R₃ = 4 cm

R₁ + R₂  = R₂ + R₃

=> R₁ = R₃

R₁ + R₃ = 4

R₁ = R₃

=> R₁ = R₃ = 2

R₁ + R₂  = 3

=> 2 + R₂  = 3

=>  R₂  = 1

Radius of circles = 2 , 1 , 2 cm

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