Question

given that qm = 15 units, sm = 10 units, and rm = 18 units, what is the length of segment pm?
a. 12 units
b. 13 units
c. 7 units
d. 8 units

Explanation:

Step1: Recall the intersecting chords theorem

The intersecting chords theorem states that if two chords intersect at a point, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord. So, if chords \( QP \) and \( RS \) intersect at \( M \), then \( QM \times PM = SM \times RM \).

Step2: Substitute the given values

We know that \( QM = 15 \) units, \( SM = 10 \) units, and \( RM = 18 \) units. Let \( PM = x \). Then according to the theorem:
\[
15\times x=10\times 18
\]

Step3: Solve for \( x \)

First, calculate the right - hand side: \( 10\times18 = 180 \). Then we have the equation \( 15x=180 \). Divide both sides by 15:
\[
x=\frac{180}{15}=12
\]

Answer:

12 units (which corresponds to option A)