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Let $P$ be a variable point on a circle $C$ and $Q$ be a fixed point outside $C$. If $R$ is the midpoint of the line segment $P Q$, then locus of $R$ is
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a circle
Let circle be $\left(x-x_{1}\right)=r \cos \theta$
$y-y_{1}=r \sin \theta$
$h=\frac{a+x_{1}+r \cos \theta}{2}$
$k=\frac{b+y_{1}+r \sin \theta}{2}$
$\Rightarrow\left(h-\frac{\left(a+x_{1}\right)}{2}\right)^{2}+\left(k-\frac{\left(b+y_{1}\right)}{2}\right)^{2}=\frac{r^{2}}{4}$
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