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

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

Options:

  1. 2
  2. 3
  3. 4
  4. 5

Correct Answer: 2

Solution: 

Using the intersecting chords theorem: AE * EB = CE * ED. Thus, 3 * 5 = 4 * ED, so 15 = 4 * ED, giving ED = 15/4 = 3.75.

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

Practice Questions

Q1
If two chords AB and CD intersect at point E inside a circle, and AE = 3, EB = 5, CE = 4, what is the length of ED?
  1. 2
  2. 3
  3. 4
  4. 5

Questions & Step-by-Step Solutions

If two chords AB and CD intersect at point E inside a circle, and AE = 3, EB = 5, CE = 4, what is the length of ED?
  • 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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