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If a chord of a circle is 16 cm long and the radius of the circle is 10 cm, what

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Question: If a chord of a circle is 16 cm long and the radius of the circle is 10 cm, what is the distance from the center of the circle to the chord?

Options:

  1. 6
  2. 8
  3. 4
  4. 10

Correct Answer: 8

Solution: 

Using the formula d = √(r^2 - (c/2)^2), where r is the radius and c is the length of the chord: d = √(10^2 - (16/2)^2) = √(100 - 64) = √36 = 6.

If a chord of a circle is 16 cm long and the radius of the circle is 10 cm, what

Practice Questions

Q1
If a chord of a circle is 16 cm long and the radius of the circle is 10 cm, what is the distance from the center of the circle to the chord?
  1. 6
  2. 8
  3. 4
  4. 10

Questions & Step-by-Step Solutions

If a chord of a circle is 16 cm long and the radius of the circle is 10 cm, what is the distance from the center of the circle to the chord?
  • Step 1: Identify the radius of the circle (r) and the length of the chord (c). Here, r = 10 cm and c = 16 cm.
  • Step 2: Calculate half the length of the chord. This is c/2 = 16 cm / 2 = 8 cm.
  • Step 3: Use the formula to find the distance (d) from the center of the circle to the chord: d = √(r^2 - (c/2)^2).
  • Step 4: Substitute the values into the formula: d = √(10^2 - 8^2).
  • Step 5: Calculate 10^2, which is 100, and 8^2, which is 64.
  • Step 6: Subtract 64 from 100: 100 - 64 = 36.
  • Step 7: Take the square root of 36: √36 = 6.
  • Step 8: The distance from the center of the circle to the chord is 6 cm.
  • Circle Geometry – Understanding the relationship between the radius, chord length, and distance from the center to the chord.
  • Pythagorean Theorem – Applying the theorem to find the distance from the center of the circle to the chord using right triangle properties.
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