1. If m RU = 30, m RS = 88, m ST = 114, find:
m∠S
m∠R
Problem of the Day

2. Section Tangents

3. Then
Now
Objectives
You used the Pythagorean Theorem to find side lengths of right triangles.
Use properties of tangents.
Solve problems involving circumscribed polygons.

4. Common Core State Standards
Content Standards.
G.CO.12 – Make formal geometric constructions with a variety of tools and methods.
G.C.4 – Construct a tangent line from a point outside a given circle to the circle.
Mathematical Practices
1) Make sense of Problems and persevere in solving them.
2) Reason abstractly and quantitatively.
Common Core State Standards

5. A tangent is a line in the same plane as a circle that intersects the circle in exactly one point, called the point of tangency.
Vocabulary

6. A common tangent is a line, ray, or segment that is tangent to two circles in the same plane. In each figure, line l is a common tangent of circles F and G.
Vocabulary

7. Draw the common tangents.
Example 1

9. Find the value of x.
Example 3

10. Find the value of x.
Example 3

11. Find the value of x.
Example 3

13. Find the value of x. Assume that segments that appear to be tangent are tangent.
Example 4

14. A polygon is circumscribed about a circle if every side of the polygon is tangent to the circle.

15. For each figure, find the value of the variable.
Example 5

16. For each figure, find the value of the variable.
Example 5

17. p.736 #4, 8, 17, 18, 24, 25, 44 – 46
Homework