1. Chapter 10: Circles
10.1: Tangents to Circles

2. Learning Outcomes
I will be able to identify segments and lines related to circles.

3. Vocabulary
Circle: A circles is a set of points that are equidistant from a given point, called the center.

4. Vocabulary
Radius: This is the distance from the center of the circle to a point on the circle.
Two circles are considered congruent if they have the same radius.

5. Vocabulary
Diameter: The diameter is the distance across the circle through the center. The diameter is twice the radius, or d = 2r.

6. Vocabulary
Chord: A chord is a segment whose endpoints are points on a circle.
In this example PR and PS are chords.

7. Vocabulary
Secant: A secant is a line that intersects a circle in two points.

8. Vocabulary
Tangent: a tangent line is a line that intersects a circle at one point. Where the tangent line intersects a circle is called a point of tangency.

9. Common Tangents Common tangents are either external or internal.
Internal External

10. Practice

11. Activity Draw a circle. Draw a line tangent to your circle.
Draw the radius to your point of tangency.
Think-Pair-Share
What do you notice about the tangent line and the radius?

12. Properties of Tangent Lines

13. Is Line EF tangent to the circle?
To determine this we use the Pythagorean Theorem to see if these three lengths form a right triangle.
11²+60² = 61²
3721 = 3721
Since these lengths form a right triangle, EF is tangent to the circle

14. Find the Radius of the circle.
r² + 16² = (r+8) ² r² = r² + 16r r² -r² 256 = 16r = 16r 12 = r The radius is 12.

15. More Properties of circles

16. Find the value of x
x² + 2 = x² = 9 x = 3

17. Exit Ticket Homework Tell whether AB is tangent to the circle.
18-28, 36-41, 46-48

18. Chapter 10.2
Arcs and Chords

19. Learning Outcomes
I will be able to use arc addition postulate to find missing arc measurements
I will be able to use properties involving congruent chord/arcs to find missing measurements.

20. Minor and Major Arcs
A minor arc is an arc that is less than 180 degrees and is typically expressed with two letters.
A major arc is an arc that is greater than 180 degrees and is typically expressed with three letters.

21. Arc Addition Postulate

22. Practice

23. Theorems

24. Theorems

25. Practice
22. We can conclude that segment AB and segment CD are equidistant from F.
23. We can conclude that segment AB is congruent to segment CB and that they are equidistant from F.
24. We can conclude that segment AD is congruent to segment BD.

26. Practice