Question

Chords AB and CD of a circle intersect inside the circle at point E. If AE = 4, EB = 10, and CE = 8, then find ED:

• A. 7
• B. 5
• C. 8
• D. 9

Hint:

For intersecting chords in a circle, remember that the products of the two segments of each chord are equal.

Answer 1

The Correct Option is D

Step 1: Apply the property of intersecting chords.
When two chords intersect inside a circle, the product of the segments of one chord equals the product of the segments of the other chord. That is:
\[ AE \times EB = CE \times ED \]
Step 2: Substitute the given values.
\[ 4 \times 10 = 8 \times ED \]
Step 3: Simplify to find ED.
\[ 40 = 8 \times ED \] \[ ED = \frac{40}{8} = 5 \] Step 4: Verify.
Thus, $ED = 5$.
Correct Answer: (B) 5