The radius will equal the distance from the center(1,5) to the point on the circle(10,10)
[tex] \sqrt{(10-1)^{2} + (10-5)^{2} } [/tex]
[tex] \sqrt{81 + 25} = \sqrt{106} [/tex]
The radius is [tex] \sqrt{106}
[/tex]
area = [tex] \pi r^{2} [/tex]
[tex]106 \pi [/tex]
503 units^2