1. Wednesday, April 26, 2017
Warm Up
1. What is the length of the diagonal of a square with side lengths ? 14
2. In a 45o45o90o triangle, what is the length of each leg if the hypotenuse is 8?
3. Find the value of x and y. x y 22
60o
4. In a 30o60o90o triangle, the shorter leg is 3.3 feet long. Find the perimeter.
5. Solve: 4x = 0

2. Properties of Tangents
Wednesday, April 26, 2017
Essential Question:
How do we use properties of a tangent to a circle?
Lesson 6.1

3. Daily Homework Quiz 1.
Give the name that best describes the figure . a. CD
secant b. AB
tangent c. FD d. EP
Chord
radius

4. Daily Homework Quiz 2.
Tell how many common tangents the circles have .
ANSWER
One tangent; it is a vertical line through the point of tangency.

5. Perpendicular Tangent Theorem 6.1
In a plane, if a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.

6. Tangent Theorems
Create right triangles for problem solving.

7. 1. Find the segment length indicated. Assume that lines which appear
tangent are tangent.

8. 2. Find the segment length indicated. Assume that lines which appear
tangent are tangent.

9. 3. Find the segment length indicated. Assume that lines which appear
tangent are tangent.

10. 4. Find the segment length indicated. Assume that lines which appear
tangent are tangent.

11. 5. Find the segment length indicated. Assume that lines which appear
tangent are tangent.

12. Write the binomial twice. Multiply.
Find the radius of a circle
6. In the diagram, ʘB is a point of tangency. Find the radius r of ʘC.
SOLUTION
You know 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 + 50)(r + 50) = r
Write the binomial twice.
Multiply.
r2 + 50r +50r = r
r r = r
Combine Like Terms.
100r = 3900
Subtract from each side.
r = 39 ft .
Divide each side by 100.

13. Subtract from each side.
Find the radius of a circle
7. ST is tangent to ʘ 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.
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.

14. Perpendicular Tangent Converse
In a plane, if a line is perpendicular to a radius of a circle at its endpoint on the circle, then the line is tangent to the circle.

15. Verify a tangent to a circle
8. Determine if line AB is tangent to the circle.

16. Verify a tangent to a circle
9. Determine if line AB is tangent to the circle.

17. GUIDED PRACTICE
Verify a tangent to a circle
Is DE tangent to ʘ 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 

18. Verify a tangent to a circle
11. In the diagram, PT is a radius of ʘ P. Is ST tangent to ʘ 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 ʘ P at its endpoint on ʘ P. ST is tangent to ʘ P.

19. Homework
Page 186 # 12 – 17.
Page 188 # 17 – 19.