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  • Two circles of radii ' a ' and 'b' touching each other externally, are inscribed in the area bounded by <img alt="\mathrm{y=\sqrt{1-x^2}}" src="https://entrancecorner.oncodecogs.com

Two circles of radii ' a ' and 'b' touching each other externally, are inscribed in the area bounded by \mathrm{y=\sqrt{1-x^2}} and the x-axis. If \mathrm{b=\frac{1}{2}}, then a is equal to

Option: 1

\frac{1}{4}


Option: 2

\frac{1}{8}


Option: 3

\frac{1}{2}


Option: 4

\frac{1}{\sqrt 2}


Answers (1)

best_answer

\mathrm{\Rightarrow \mathrm{C}_1 \: is \: (\sqrt{1-2 \mathrm{a}}, \mathrm{a}) \: and\: \mathrm{C}_2\: is \: (\sqrt{1-2 b}, b) }

\mathrm{\begin{aligned} & \Rightarrow C_1 C_2=a+b=a+\frac{1}{2} \\ & \Rightarrow 1-2 a+\left(a-\frac{1}{2}\right)^2=\left(a+\frac{1}{2}\right)^2 \\ & \Rightarrow a=\frac{1}{4} . \end{aligned} }

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Ritika Kankaria

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