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Question: C, C<sub>1</sub>, C<sub>2</sub> are circles of radii 5, 3, 2 respectively. C<sub>1</sub> and C<sub>2...

C, C1, C2 are circles of radii 5, 3, 2 respectively. C1 and C2 touch each other externally and C internally. The radius of circle C3 which touches C internally and C1 and C2 externally is-

A

3/2

B

20/9

C

35/19

D

30/19

Answer

30/19

Explanation

Solution

Let O, O1, O2, O3 be the centres of the circles C, C1, C2, C3 respectively and r the desired radius of C3.

O1O = 2, OO2 = 3, O1O3 = r +3, OO3 = 5 – r, O2O3 = r + 2

by cosine rule applied to find O1O3 and O2O3

we get r = 3019\frac{30}{19}