Let a , b , r ∈ R {\displaystyle {}a,b,r\in \mathbb {R} } , r > 0 {\displaystyle {}r>0} , and let
be the circle with center M = ( a , b ) {\displaystyle {}M=(a,b)} and radius r {\displaystyle {}r} . Let G {\displaystyle {}G} denote a line in R 2 {\displaystyle {}\mathbb {R} ^{2}} with the property that there exists at least one point P {\displaystyle {}P} on G {\displaystyle {}G} such that d ( M , P ) ≤ r {\displaystyle {}d(M,P)\leq r} . Show that K ∩ G ≠ ∅ {\displaystyle {}K\cap G\neq \emptyset } .
,
,
and let
and radius 
. Let 
denote a line in 
with the property that there exists at least one point 
on such that
.
Show that
.
