A circle passes through the points (2,3) and (4,5). If its centre lies on the line y - x + 3 = 0, then its radius is equal to √5 or √2

Equation of the line through the given points is y - 3 = (5-3)/(4-2)(x - 2) which simplifies to y - 3 = x - 2 => x - y + 1 = 0.
Equation of the perpendicular line through the midpoint (3,4) is y - 4 = -1(x - 3) => x + y - 7 = 0. This intersects the given line y - x + 3 = 0 at the center of the circle. Subtracting the two equations gives 2y - 10 = 0 => y = 5. Substituting y = 5 into x + y - 7 = 0 gives x = 2. So, the center of the circle is (2,5).
Clearly, the radius is then √((2-2)² + (5-3)²) = √(0² + 2²) = 2 units. Also, √((2-4)² + (5-5)²) = √((-2)² + 0²) = 2 units.
√((2-4)²+(5-3)²)=√8. √((4-2)²+(5-3)²)=√8. Therefore the radius is 2 units.
So the answer is option A (if corrected to 2).