Answer:
[tex]QP=20\ units[/tex]
Step-by-step explanation:
The picture of the question in the attached figure
Let
O ---> the center of the circle
we have that
Line segment QP is tangent to the circle
That means
OQ (radius) is perpendicular to segment QP
OQP is a right triangle
Applying Pythagorean Theorem
[tex]OP^2=OQ^2+QP^2[/tex]
we have
The radius is equal to
[tex]r=24/2=12\ units[/tex] ----> the radius is half the diameter
[tex]OP=r+NP=12+11.5=23.5\ units[/tex]
[tex]OQ=r=12\ units[/tex]
substitute
[tex]23.5^2=12^2+QP^2[/tex]
[tex]QP^2=23.5^2-12^2[/tex]
[tex]QP^2=408.25[/tex]
[tex]QP=20\ units[/tex]
