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Q.

Inside a semi-circle of radius 1 unit, two circles of radii r1 and r2 are drawn, each touching the circumference and the diameter of the semi-circle also touches each other externally. Then [max.(r1 + r2)] where [x] denotes integral value nearest to x .............

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Detailed Solution

Centres of the smaller circles be C1a,r1,C2b,r2

OC1=R−r1⇒1−a2=2r1

Also, 1−b2=2r2

and C1C2=r1+r2

⇒(a−b)2=4r1r2

Also, r1+r2=1−a2+b22<1−|a|b

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