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If two chords AB and CD of a circle intersect at point E, and AE = 3 cm, EB = 5

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Question: If two chords AB and CD of a circle intersect at point E, and AE = 3 cm, EB = 5 cm, what is the length of segment CE if ED = 4 cm?

Options:

  1. 6 cm
  2. 8 cm
  3. 12 cm
  4. 10 cm

Correct Answer: 8 cm

Solution: 

According to the intersecting chords theorem, AE * EB = CE * ED. Thus, 3 * 5 = CE * 4, which gives CE = (15/4) = 3.75 cm.

If two chords AB and CD of a circle intersect at point E, and AE = 3 cm, EB = 5

Practice Questions

Q1
If two chords AB and CD of a circle intersect at point E, and AE = 3 cm, EB = 5 cm, what is the length of segment CE if ED = 4 cm?
  1. 6 cm
  2. 8 cm
  3. 12 cm
  4. 10 cm

Questions & Step-by-Step Solutions

If two chords AB and CD of a circle intersect at point E, and AE = 3 cm, EB = 5 cm, what is the length of segment CE if ED = 4 cm?
  • Intersecting Chords Theorem – This theorem states that if two chords intersect inside a circle, the products of the lengths of the segments of each chord are equal.
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