Question

PG¯¯¯¯¯¯¯¯=9 in. The radius of the circle is 41 inches. Find the length of CT¯¯¯¯¯¯¯.

A. 40
B. 9
C. 80
D. not enough information

Answer 1

Option: C is the correct answer.

C. 80

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.

`CP^2=CS^2+SP^2\\\\i.e.\\\\`

as CP is the radius of the circle

and SP=PG=9 in.

i.e.

`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`

and

similarly in right angled triangle ΔPST

we have:

`TP^2=ST^2+PS^2\\\\i.e.\\\\41^2=9^2+ST^2\\\\i.e.\\\\ST=40\ units`

Hence,

`CT=CS+ST\\\\i.e.\\\\CT=40+40\\\\i.e.\\\\CT=80\ in.`

Answer 2

See the attached picture for the solution.