Question 965296
The square is centered about the origin. 
The vertex makes an angle of 45 degrees to the x-axis so it lies on the line {{{y=x}}}
.
.
Substituting, 
{{{x^2+y^2=25}}}
{{{x^2+x^2=25}}}
{{{2x^2=25}}}
{{{x^2=25/2}}}
{{{x=5/sqrt(2)}}}
{{{y=(5sqrt(2))/2}}}
So the coordinates are,
({{{( 5sqrt(2))/2 }}},{{{(5sqrt(2))/2}}})
({{{(-5sqrt(2))/2}}},{{{(5sqrt(2))/2}}})
({{{(-5sqrt(2))/2}}},{{{(-5sqrt(2))/2}}})
({{{(5sqrt(2))/2}}},{{{(-5sqrt(2))/2}}})
{{{drawing(300,300,-6,6,-6,6,grid(1),
line((5sqrt(2))/2,(5sqrt(2))/2,(5sqrt(2))/2,(-5sqrt(2))/2),
line((5sqrt(2))/2,(-5sqrt(2))/2,(-5sqrt(2))/2,(-5sqrt(2))/2),
line((-5sqrt(2))/2,(-5sqrt(2))/2,(-5sqrt(2))/2,(5sqrt(2))/2),
line((-5sqrt(2))/2,(5sqrt(2))/2,(5sqrt(2))/2,(5sqrt(2))/2),
circle(0,0,5),graph(300,300,-6,6,-6,6,x))}}}