Let the diameter of a subset S of the plane be defined as the maximum of the distance between arbitrary of points of S

Question

Let the diameter of a subset S of the plane be defined as the maximum of the distance between arbitrary of points of S.

Let$$S=\{(x,y):(y-x)\le0,(x+y)\ge0,x^2+y^2\le2\}$$

Then the diameter of S is '2'.

I am unable to gain thaat solution.

Thanks in advance !

Answer 1

Your set $S$ is the part of circle of radius $\sqrt2$ between the bisectrices of the first and fourth quadrants.

So his diameter is the distance between the points $(1,1)$ and $(1,-1)$ (black points on the circe) : $d=2$.