What is the relationship between the angles subtended by the same arc at the cen

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

Options:

Correct Answer: The angle at the center is twice that at the circumference.

Solution:

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

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

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

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.

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