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If a line segment is drawn from the center of a circle to the midpoint of a chor

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Question: If a line segment is drawn from the center of a circle to the midpoint of a chord, what can be said about this line segment?

Options:

  1. It is perpendicular to the chord.
  2. It bisects the chord.
  3. It is the radius.
  4. It is the diameter.

Correct Answer: It is perpendicular to the chord.

Solution:

A line segment drawn from the center of a circle to the midpoint of a chord is perpendicular to the chord.

If a line segment is drawn from the center of a circle to the midpoint of a chor

Practice Questions

Q1
If a line segment is drawn from the center of a circle to the midpoint of a chord, what can be said about this line segment?
  1. It is perpendicular to the chord.
  2. It bisects the chord.
  3. It is the radius.
  4. It is the diameter.

Questions & Step-by-Step Solutions

If a line segment is drawn from the center of a circle to the midpoint of a chord, what can be said about this line segment?
  • Step 1: Understand what a circle is. A circle is a round shape where all points are the same distance from the center.
  • Step 2: Identify the center of the circle. This is the point in the middle of the circle.
  • Step 3: Know what a chord is. A chord is a straight line that connects two points on the edge of the circle.
  • Step 4: Find the midpoint of the chord. The midpoint is the point that is exactly in the middle of the chord.
  • Step 5: Draw a line segment from the center of the circle to the midpoint of the chord. This is the line we are talking about.
  • Step 6: Understand the relationship between the line segment and the chord. The line segment from the center to the midpoint of the chord creates a right angle (90 degrees) with the chord.
  • Perpendicularity in Circles – A line segment from the center of a circle to the midpoint of a chord is always perpendicular to that chord.
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