Answer:
The length of segment PQ is [tex]5\ units[/tex]
Step-by-step explanation:
we know that
Applying the Intersecting Tangent-Secant Theorem
[tex]MN^{2}=PN*QN[/tex]
we have
[tex]MN=6\ units[/tex]
[tex]PN=(x+4)\ units[/tex]
[tex]QN=4\ units[/tex]
substitute
[tex]6^{2}=(x+4)*4[/tex]
[tex]36=4x+16[/tex]
[tex]4x=36-16[/tex]
[tex]4x=20[/tex]
[tex]x=5\ units[/tex]
therefore
The length of segment PQ is [tex]5\ units[/tex]
