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

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

Options:

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

Correct Answer: 8 cm

Solution: 

Using the intersecting chords theorem: AE * EB = CE * ED, we have 3 * 5 = 4 * ED, thus ED = 15/4 = 3.75 cm.

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

Practice Questions

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

Questions & Step-by-Step Solutions

Two chords AB and CD of a circle intersect at point E. If AE = 3 cm, EB = 5 cm, and CE = 4 cm, 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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