For MN to be tangent, angle N would need to be 90 degrees making the triangle a right triangle.
Using the Pythagorean theorem uses the base and the height to see if it equals what is shown for the hypotenuse. If it does it is tangent.
Hypotenuse = SQRT(18^2 + 80^2)
Hypotenuse = sqrt(324 + 6400)
Hypotenuse = sqrt(6724)
Hypotenuse = 82
This matches the 82 shown in the picture, so it is a right triangle, making MN tangent to circle L.
