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What is the measure of the angle subtended by an arc at the center of a circle c

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Question: What is the measure of the angle subtended by an arc at the center of a circle compared to the angle subtended at any point on the remaining part of the circle?

Options:

  1. Half the angle at the center
  2. Equal to the angle at the center
  3. Twice the angle at the center
  4. None of the above

Correct Answer: Half the angle at the center

Solution: 

The angle subtended by an arc at the center of a circle is twice the angle subtended at any point on the remaining part of the circle.

What is the measure of the angle subtended by an arc at the center of a circle c

Practice Questions

Q1
What is the measure of the angle subtended by an arc at the center of a circle compared to the angle subtended at any point on the remaining part of the circle?
  1. Half the angle at the center
  2. Equal to the angle at the center
  3. Twice the angle at the center
  4. None of the above

Questions & Step-by-Step Solutions

What is the measure of the angle subtended by an arc at the center of a circle compared to the angle subtended at any point on the remaining part of the 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 connect the center of the circle to the endpoints of the arc.
  • Step 4: Note that this angle at the center is called the central angle.
  • Step 5: Now, consider a point on the remaining part of the circle (not at the center). This point can also form an angle with the endpoints of the arc.
  • Step 6: This angle formed at the point on the circle is called the inscribed angle.
  • Step 7: The key relationship is that the central angle is always twice the inscribed angle for the same arc.
  • Step 8: Therefore, if you know the inscribed angle, you can find the central angle by multiplying it by 2.
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