Answer:
Part a) [tex]PM=6\ in[/tex]
Part b) [tex]PQ=12\ in[/tex]
Step-by-step explanation:
step 1
we know that
The diameter of the circle divide the circle into two equal parts
so
PM=MQ
Applying the Intersecting Chord Theorem (When two chords intersect each other inside a circle, the products of their segments are equal)
[tex]SM*RM=PM*MQ[/tex]
[tex]SM*RM=PM^{2}[/tex]
we have
[tex]SM=13-4=9\ in[/tex]
[tex]RM=4\ in[/tex]
substitute
[tex]9*4=PM^{2}[/tex]
[tex]PM^{2}=36[/tex]
[tex]PM=6\ in[/tex]
step 2
Find the value of PQ
we know that
[tex]PM=MQ[/tex]
so
[tex]PQ=PM+MQ[/tex]
[tex]PQ=2PM[/tex]
we have
[tex]PM=6\ in[/tex]
substitute
[tex]PQ=2(6)=12\ in[/tex]
