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In a circle, if a chord is drawn, which of the following statements is true rega

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Question: In a circle, if a chord is drawn, which of the following statements is true regarding the angles formed?

Options:

  1. The angles subtended by the chord at the center are equal.
  2. The angles subtended by the chord at the circumference are equal.
  3. The angles subtended at the center are half of those at the circumference.
  4. The angles subtended at the circumference are equal to those at the center.

Correct Answer: The angles subtended by the chord at the circumference are equal.

Solution: 

The angles subtended by the same chord at the circumference are equal.

In a circle, if a chord is drawn, which of the following statements is true rega

Practice Questions

Q1
In a circle, if a chord is drawn, which of the following statements is true regarding the angles formed?
  1. The angles subtended by the chord at the center are equal.
  2. The angles subtended by the chord at the circumference are equal.
  3. The angles subtended at the center are half of those at the circumference.
  4. The angles subtended at the circumference are equal to those at the center.

Questions & Step-by-Step Solutions

In a circle, if a chord is drawn, which of the following statements is true regarding the angles formed?
  • Step 1: Understand what a chord is. A chord is a straight line that connects two points on the circumference of a circle.
  • Step 2: Identify the points where the chord intersects the circumference. Let's call these points A and B.
  • Step 3: Recognize that when you draw lines from points A and B to any other point C on the circumference, you create angles.
  • Step 4: Note that if you draw another point D on the circumference and connect it to points A and B, you create another angle.
  • Step 5: The key idea is that the angles formed at points C and D by the same chord AB are equal.
  • Step 6: This means that no matter where you place point C or D on the circumference, as long as they are connected to the same chord AB, the angles will always be the same.
  • Angles Subtended by a Chord – The angles formed at the circumference of a circle by the same chord are equal, which is a fundamental property of circles.
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