Question

A circle is shown below.
If FM = 11, MG = 3, and PM = 2, what is the measure of PQ?
A. 7.3
B. 9.3
C. 16.5
D. 18.5

Answer 1

Answer:

D. 18.5

Step-by-step explanation:

Given:

FM = 11

MG = 3

PM = 2,

Required:

Measure of PQ

SOLUTION:

PQ = PM + MQ

We know that, PM = 2. But we don't know the measure of MQ.

Based on the Intersecting Chords Theorem,

$FM*MG = PM*MQ$

Plug in the values

$11*3 = 2*MQ$

$33 = 2*MQ$

Divide both sides by 2

$\frac{33}{2} = MQ$

$16.5 = MQ$

MQ = 16.5

✍️PQ = PM + MQ

Plug in the values

PQ = 2 + 16.5

PQ = 18.5