Answer:
[tex]PQ=9.6\ units[/tex]
Step-by-step explanation:
In this problem
If AB=31.8 units
then
ZY=31.8 units
ZP=PY=31.8/2=15.9 units
In the right triangle MZP
we have
[tex]ZP=15.9\ units[/tex]
[tex]MZ=18\ units[/tex] ----> the radius of the circle
Applying Pythagoras Theorem Find MP
[tex]MP^{2}=MZ^{2}-ZP^{2}[/tex]
substitute
[tex]MP^{2}=18^{2}-15.9^{2}[/tex]
[tex]MP^{2}=71.19[/tex]
[tex]MP=8.4\ units[/tex]
Find the value of PQ
we know that
[tex]MQ=MP+PQ\\ PQ=MQ-MP[/tex]
we have
[tex]MQ=18\ units[/tex]
[tex]MP=8.4\ units[/tex]
substitute
[tex]PQ=18-8.4=9.6\ units[/tex]
