In the given figure, O is the center of the circle. If OM = 20 and MN = 12, find the radius of the circle.

Solution:

We are given a circle with center O. M and N are points on the circle. OM is the radius of the circle, and MN is a chord of the circle.

We are given:

• OM = 20 (This is the radius of the circle, denoted by r)
• MN = 12 (This is the length of the chord)

In the figure, the shaded region represents a segment of the circle. The line segment OM is shown as a radius, with a length of 20. The line segment MN is shown as a chord with length 12. The question asks for the radius of the circle.

From the given information, OM is the radius of the circle, and its length is given as 20.

Therefore, the radius of the circle is 20.

Answer: The radius of the circle is 20.