What is the relationship between the angles subtended by the same arc at the center and at the circumference of a circle?

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Q: What is the relationship between the angles subtended by the same arc at the center and at the circumference of a circle?

Solution: The angle subtended at the center is always twice that subtended at the circumference.

Steps: 7

Step 1: Understand what an arc is. An arc is a part of the circumference of a circle.
Step 2: Identify the center of the circle. This is the point that is equidistant from all points on the circle.
Step 3: Recognize that an angle can be formed by two lines (radii) that meet at the center of the circle.
Step 4: Note that the same arc can also create an angle at any point on the circumference of the circle.
Step 5: Measure the angle formed at the center of the circle by the two radii that connect to the endpoints of the arc.
Step 6: Measure the angle formed at the circumference by the lines connecting the endpoints of the arc to a point on the circumference.
Step 7: Compare the two angles. You will find that the angle at the center is always twice the angle at the circumference.