Euclidean plane/Circle and piercing line/Cut/Exercise

Let ${}a,b,r\in \mathbb {R}$, ${}r>0$, and let

${}K={\left\{(x,y)\in \mathbb {R} ^{2}\mid (x-a)^{2}+(y-b)^{2}=r^{2}\right\}}\,$

be the circle with center ${}M=(a,b)$ and radius ${}r$. Let ${}G$ denote a line in ${}\mathbb {R} ^{2}$ with the property that there exists at least one point ${}P$ on ${}G$ such that ${}d(M,P)\leq r$. Show that

${}K\cap G\neq \emptyset$.

Create a solution