Pythagorean Theorem states that:
[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]
If a = 5, and b = 5, then:
[tex] {c}^{2} = {5}^{2} + {5}^{2} [/tex]
[tex]so \: c = \sqrt{( {5}^{2} + {5}^{2}) } = \sqrt{50} \\ = \sqrt{25} \times \sqrt{2} = 5 \sqrt{2} [/tex]
The equation of that circle, where origin is center, is:
[tex] {x}^{2} + {y}^{2} = {r}^{2} \\ where \: r = radius \\ so \: {x}^{2} + {y}^{2} = {5}^{2} \\ {x}^{2} + {y}^{2} = 25[/tex]
That point (5, 5) lies directly on this circle.
