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 $C$…

Question

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

Aicharya · Accepted Answer

$(r+1)^2=\alpha^2+9$ $ \begin{array}{lc} \Rightarrow & r^2+8=\alpha^2 \ \Rightarrow & r^2+2 r+1=r^2+8+9 \ \Rightarrow & 2 r=16 \Rightarrow r=8 \end{array} $

The centres of two circles $C_1$ and $C_2$ each of unit radius are at a distance of 6 units from each other.…

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