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Question

Three circle touch each other externally. A triangle is formed when the centres of these circles are joined together. Find the radii of the circles, if the sides of the triangle formed are 6 cm, 8 cm and 9 cm


A

r2=5.5 cm
r3=3.5 cm
r1=3.5 cm

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B

r2=5.9 cm
r3=3.5 cm
r1=2.5 cm

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C

r2=5.9 cm
r3=1.5 cm
r1=2.5 cm

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D

r2=5.9 cm
r3=9.5 cm
r1=2.5 cm

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Solution

The correct option is A

r2=5.5 cm
r3=3.5 cm
r1=3.5 cm


Three circle touches each other externally
Δ ABC is formed by joining the centres, A, B and C of the circles.
AB = 6 cm, AC = 8 cm and BC = 9 cm

Let radii of the circles having centres A, B and C
be r1,r2,r3 respectively
r1+r3=8,r3+r2=9,r1+r2=6
Adding r1+r3+r3+r2+r1+r2=6+8+9 cm2(r2+r2+r3)=23
r1+r2+r3=232=11.5 cm
r1+9=11.5 cm
r1=11.59=2.5 cm
r2+6=11.5r2=11.56=5.5 cm
r3=11.5r3=11.58=3.5 cm
r1=2.5 cmr2=2.5 and r3=3.5 cm


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