Multiple choice

The chords AB and CD of a circle intersect at E. If AE = 12 cm, BE = 20.25 cm and CE = 3 DE, then the length (in cm) of CE is:

  1. 27

  2. 25.5

  3. 18

  4. 28.5
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A Correct answer
Explanation

Using the Intersecting Chords Theorem: AE × BE = CE × DE. Given AE=12, BE=20.25, and CE=3DE. Let CE=3x, DE=x. Then 12 × 20.25 = 3x × x, so 243 = 3x², giving x²=81 and x=9. Therefore CE=27 cm.

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