Question

two chords intersect in the interior of a circle. one chord is divided into two segments measuring 8 units and 9 units. the other chord is divided into two segments, one of which measures 3 units. what is the measure of the other segment? a. 4 units b. 12 units c. 14 units d. 16 units e. 24 units

Explanation:

Step1: Recall intersecting chords theorem

When two chords intersect in a circle, the product of the lengths of the segments of one chord equals the product of the lengths of the segments of the other chord. Let the unknown segment length be $x$.

Step2: Set up equation using theorem

The product of the first chord's segments is $8 \times 9$, and the product of the second chord's segments is $3 \times x$. Set them equal:
$$8 \times 9 = 3 \times x$$

Step3: Solve for $x$

First calculate $8 \times 9 = 72$. Then rearrange to solve for $x$:
$$x = \frac{72}{3}$$
$$x = 24$$

Answer:

E. 24 units