Multiple choice

In a circle of radius 11 cm, CD is a diameter and AB is a chord of length 20.5 cm. If AB and CD intersect at a point E inside the circle and CE has length 7 cm, then the difference of the lengths of BE and AE, in cm, is

  1. 0.75

  2. 0.5

  3. 1.25

  4. 15
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the intersecting chords theorem: AE × BE = CE × ED. With CD as diameter of length 22 cm, CE = 7 cm, so ED = 15 cm. Also AE + BE = 20.5 cm. Let AE = x, then BE = 20.5-x. Then x(20.5-x) = 7×15 = 105. Solving: x²-20.5x+105=0 gives x=10 or x=10.5. Thus BE-AE = 10.5-10 = 0.5 cm. The answer is option B.

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