1. Sect. 10.1 Tangents to Circles
Goal Communicating About Circles
Goal Using Properties of Tangents

2. Communicating About Circles
Circle Terminology:
A CIRCLE is the set of all points in the plane that are a given distance from a given point.  The given point is called the CENTER of the circle.
A circle is named by its center point.
“Circle A”
or A

3. Parts of a Circle Tangent Radius Chord Diameter Secant
Communicating About Circles
Parts of a Circle
Tangent
Radius
Chord
Diameter
Secant

4. Communicating About Circles
Example 1:
Tell whether each segment is best described as a chord, secant, tangent, diameter, or radius A
Secant
Radius
Chord
Diameter

5. Communicating About Circles
In a plane, two circles can intersect in two points, one point, or no points.
One Point
Two Points
Coplanar Circles that intersect in one point are called Tangent Circles
No Point

6. Communicating About Circles
Tangent Circles
A line tangent to two coplanar circles is called a Common Tangent

7. Communicating About Circles
Concentric Circles
Two or more coplanar circles that share the same center.

8. Common External Tangents
Communicating About Circles
Common External Tangents
Common Internal Tangents
Common External Tangent does not intersect the segment joining the centers of the two circles.
Common Internal Tangent intersects the segment joining the centers of the two circles.

9. Interior Exterior On the circle
Communicating About Circles
A circle divides a plane into three parts
Interior
Exterior
On the circle

10. External Tell whether the common tangent is Internal or External.
Communicating About Circles
Example 2:
Tell whether the common tangent is Internal or External.
External

11. Common tangents: x = 4; y = 4; and y = 0
Communicating About Circles
Example 3:
Find the center and radius of each circle. Describe the intersection of the two circles and describe all common tangents.
Center G: (2, 2)
Radius = 2
Center H: (6, 2)
Common tangents: x = 4; y = 4; and y = 0

12. Using Properties of Tangents
Theorem 10.1 and 10.2
If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.
The Converse then states:  In a plane, if a line is perpendicular to a radius of a circle at the endpoint on the circle, then the line is a tangent of the circle.

13. Is TS tangent to R? Explain
Using Properties of Tangents
Example 4:
Is TS tangent to R? Explain

14. Using Properties of Tangents
Example 5:
You are standing 14 feet from a water tower. The distance from you to a point of tangency on the tower is 28 feet. What is the radius of the water tower?
Radius = 21 feet

15. Using Properties of Tangents
Theorem 10.3
If two segments from the same exterior point are tangent to the circle, then they are congruent.

16. Using Properties of Tangents
Example 6:
is tangent to R at S is tangent to R at V. Find the value of x.
x2 - 4
x = 5 or -5

17. Using Properties of Tangents
Example 7:
is tangent to R at S is tangent to R at V. Find the value of x.
x2 + 8
x = 6 or -6

18. x = 39 y = 15 z = 36 Find the values of x, y, and z in the diagram.
Using Properties of Tangents
Example 8:
Find the values of x, y, and z in the diagram.
x = 39 y = 15 z = 36