Multiple choice

Chords $AB$ and $CD$ of a circle intersect inside the circle at point $E$.If $AE=5.6,EB=10,CE=8,$ find ED.

  1. $7$
  2. $8$
  3. $11.2$
  4. $9$
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A Correct answer
Explanation

For chords intersecting inside a circle, the product of the segments of one chord equals the product of the segments of the other. AE * EB = CE * ED. 5.6 * 10 = 8 * ED. 56 = 8 * ED, so ED = 7.

AI explanation

When two chords intersect inside a circle, the intersecting chords theorem states that the products of their segments are equal. This gives the equation AE * EB = CE * ED. Substituting the values results in 5.6 * 10 = 8 * ED, which simplifies to 56 = 8 * ED. Dividing by 8 gives ED = 7.

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