Question

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

Explanation:

Step1: Apply the intersecting - chords theorem

If two chords $PQ$ and $RS$ intersect at a point $M$ inside a circle, then $QM\times PM=RM\times SM$.
Let $PM = x$. We know that $QM = 15$, $SM = 10$, and $RM = 18$. So, $15\times x=18\times10$.

Step2: Solve for $x$

We have the equation $15x = 180$. Divide both sides of the equation by 15: $x=\frac{180}{15}=12$.

Answer:

C. 12 units