The radius of a circle with …

The point (2,5) lies inside the circle.

To check whether a point lies inside or outside the circle, we write the equation of circle and substitute the point in the equation.
If the value of the equation is equal to r² then the point lies on the circle.
If the value of equation is less than r² then it lies inside the circle.
And if the value of the equation is greater than r² then it lies outside the circle.
Writing the equation of circle first,
(x -h)² +(x-k)² = r² , where (h,k) is the center of circle and r is the radius of the circle.

Substituting the  values we get,

(x -(-2))² +(x-3)² = 5²
Above equation is the equation of the circle.
Now we have to find whether the point lies inside or outside the circle, we substitute the point in the equation of circle.

(2 -(-2))² +(5-3)² = 5²
16+4 = 20 , which is less than r² = 5² =25.

Therefore the point (2,5) lies inside the circle.