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If a circle passing through $(1,-2)$ has $x-y=2$ and $2 x+$ $3 y=14$ as its diameters, then the radius of the circle is
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$5$
$\begin{aligned} & x-y=2 \\ & \therefore \quad y=x-2 \\ & \text { and } 2 x+3 y=14 \\ & 2 x+3(x-2)=14 \\ & 5 x=20 \Rightarrow x=4 \\ & \therefore \quad y=4-2=2 \text {. } \\ & \therefore \quad \text { Centre is }(4,2) \text {. } \\ & \text { Radius }=\sqrt{(4-1)^2+(2+2)^2}=\sqrt{9+16}=\sqrt{25}=5 \text {. } \\ & \end{aligned}$
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