Hello there. To solve this question, we'll need to remember some properties about chords in a circle.
For this question specifically, we'll need chord-chord power theorem:
If two chords in a circle intersect at a point P, the product of the measures of one chord is equal to the product of the measures of the second chord, as in the drawing below:
The theorem says that A * B = C * D
In the case of the question, the chords FG and PQ intersects at the point M.
The measures of FM, MG and PM are given: 8, 7 and 14, respectively.
By the theorem above, we know that:
FM * MG = PM * MQ
We want to find the measure of PQ
In this case, know that PQ = PM + MQ (2)
Solving for MQ, we have:
8 * 7 = 14 * MQ
56 = 14 MQ
Divide both sides of the equation by a factor of 14
MQ = 4
By (2), we have that:
PQ = 14 + 4 = 18.
This is the measure of the chord PQ.