SATHEE: Circle 3 Question 23

Circle 3 Question 23

23. The centres of two circles $C_{1}$ and $C_{2}$ each of unit radius are at a distance of 6 units from each other. Let $P$ be the mid-point of the line segment joining the centres of $C_{1}$ and $C_{2}$ and $C$ be a circle touching circles $C_{1}$ and $C_{2}$ externally. If a common tangents to $C_{1}$ and $C$ passing through $P$ is also a common tangent to $C_{2}$ and $C$ , then the radius of the circle $C$ is …

(2009)

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Solution:

$(r + 1)^{2} = α^{2} + 9$

$\begin{aligned} r^{2} + 8 = α^{2} \\ \Rightarrow r^{2} + 2 r + 1 = r^{2} + 8 + 9 \\ \Rightarrow 2 r = 16 \Rightarrow r = 8 \end{aligned}$

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Circle 3 Question 23

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