three circles with centre a b and c touch each other externally.if ab=3 bc= 3 ca=4 then find radii of each circle
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2 cm 1cm 1cm
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Given: three circles with centre a b and c touch each other externally and ab=3 bc= 3 ca=4
To find : Radii of each circle
Solution :
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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