Circle O has a radius 28. Radii OM and ON form an angle of 60 degrees. Find MN.

A) 28 radical 2
B) 28
C) 56
D) 56 radical 3
Is it A) ?

To find the length of MN, we need to apply basic trigonometry to the given information.

First, let's consider triangle MON. We know that triangle MON is an equilateral triangle because all sides are radii of circle O and the angle MON is 60 degrees. Therefore, all three sides of the triangle are the same length.

Since the radius of circle O is 28, the length of OM (or ON) is also 28.

Next, we need to find the length of MN. To do this, we can divide triangle MON into two congruent right triangles. By drawing a perpendicular from M to the line segment ON, we create a right triangle MNO. Since triangle MON is equilateral, the perpendicular bisects ON at a right angle.

Now, we can use basic trigonometry to find the length of MN. In right triangle MNO, the length of the hypotenuse MN is equal to twice the length of one of the triangle's legs, which is 2 times 28 (since OM and ON are both 28).

Therefore, the length of MN is 2 * 28 = 56.

So, the correct answer is C) 56.