Distance Between Intersection Points on Circle

Consider a circle with center at point (1, -2) and a radius of 5 units. A line is drawn from the center of the circle at a 45-degree angle to the horizontal axis. This line intersects the circle at two points. What is the distance between these two points of intersection?

To find the distance between the points where the line intersects the circle, we can use the equation of the circle and the equation of the line.

The equation of the circle is given by:

$$ (x - 1)^2 + (y + 2)^2 = 25 $$

Determine the coordinates of the intersection points and find their distance.