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

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Question: If two chords AB and CD intersect at point E inside a circle, and AE = 3 cm, EB = 4 cm, what is the length of segment CE if DE = 2 cm?

Options:

  1. 6 cm
  2. 8 cm
  3. 5 cm
  4. 7 cm

Correct Answer: 6 cm

Solution: 

By the intersecting chords theorem, AE * EB = CE * DE. Thus, 3 * 4 = CE * 2, which gives CE = 6 cm.

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

Practice Questions

Q1
If two chords AB and CD intersect at point E inside a circle, and AE = 3 cm, EB = 4 cm, what is the length of segment CE if DE = 2 cm?
  1. 6 cm
  2. 8 cm
  3. 5 cm
  4. 7 cm

Questions & Step-by-Step Solutions

If two chords AB and CD intersect at point E inside a circle, and AE = 3 cm, EB = 4 cm, what is the length of segment CE if DE = 2 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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