Answer:
Option: C is the correct answer.
C. 80
Step-by-step explanation:
PG=9 in. The radius of the circle is 41 inches.
We know that the side CT is given by:
CT=CS+ST
The side CS is calculated by using the Pythagorean Theorem in ΔCSP
i.e.
[tex]CP^2=CS^2+SP^2\\\\i.e.\\\\[/tex]
as CP is the radius of the circle
and SP=PG=9 in.
i.e.
[tex]41^2=9^2+CS^2\\\\i.e.\\\\1681=81+CS^2\\\\i.e.\\\\CS^2=1681-81\\\\i.e.\\\\CS^2=1600\\\\i.e.\\\\CS=40\ units[/tex]
and
similarly in right angled triangle ΔPST
we have:
[tex]TP^2=ST^2+PS^2\\\\i.e.\\\\41^2=9^2+ST^2\\\\i.e.\\\\ST=40\ units[/tex]
Hence,
[tex]CT=CS+ST\\\\i.e.\\\\CT=40+40\\\\i.e.\\\\CT=80\ in.[/tex]
