1. EXAMPLE 4
Verify a tangent to a circle
In the diagram, PT is a radius of P. Is ST tangent to P ?
SOLUTION
Use the Converse of the Pythagorean Theorem. Because = 372, PST is a right triangle and ST PT . So, ST is perpendicular to a radius of P at its endpoint on P. By Theorem 10.1, ST is tangent to P.

2. Find the radius of a circle
EXAMPLE 5
Find the radius of a circle
In the diagram, B is a point of tangency. Find the radius r of C.
SOLUTION
You know from Theorem 10.1 that AB BC , so ABC is a right triangle. You can use the Pythagorean Theorem.
AC2 = BC2 + AB2
Pythagorean Theorem
(r + 50)2 = r
Substitute.
r r = r
Multiply.
100r = 3900
Subtract from each side.
r = 39 ft .
Divide each side by 100.

3. Find the radius of a circle
EXAMPLE 6
Find the radius of a circle
RS is tangent to C at S and RT is tangent to C at T. Find the value of x.
SOLUTION
RS = RT
Tangent segments from the same point are
28 = 3x + 4
Substitute.
8 = x
Solve for x.

4. GUIDED PRACTICE
for Examples 4, 5 and 6
7. Is DE tangent to C?
ANSWER
Yes – The length of CE is 5 because the radius is 3 and the outside portion is 2. That makes ∆CDE a Right Triangle. So DE and CD are

5. GUIDED PRACTICE
for Examples 4, 5 and 6
8. ST is tangent to Q.Find the value of r.
SOLUTION
You know from Theorem 10.1 that ST QS , so QST is a right triangle. You can use the Pythagorean Theorem.

6. GUIDED PRACTICE for Examples 4, 5 and 6 QT2 = QS2 + ST2
Pythagorean Theorem
(r + 18)2 = r
Substitute.
r2 + 36r = r
Multiply.
36r = 252
Subtract from each side.
r = 7
Divide each side by 36.

7. GUIDED PRACTICE for Examples 4, 5 and 6 9. Find the value(s) of x.
SOLUTION
Tangent segments from the same point are
9 = x2
Substitute.
+3 = x
Solve for x.