1. Geometry
Section 10.1

3. EXAMPLE 1
Identify special segments and lines
Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of C. AC a.
SOLUTION
is a radius because C is the center and A is a point on the circle. AC a.

4. EXAMPLE 1
Identify special segments and lines
Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of C. b. AB
SOLUTION b. AB
is a diameter because it is a chord that contains the center C.

5. EXAMPLE 1
Identify special segments and lines
Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of C. DE c.
SOLUTION c. DE
is a tangent ray because it is contained in a line that intersects the circle at only one point.

6. EXAMPLE 1
Identify special segments and lines
Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of C. AE d.
SOLUTION d. AE
is a secant because it is a line that intersects the circle in two points.

8. EXAMPLE 2
Find lengths in circles in a coordinate plane
Use the diagram to find the given lengths. a.
Radius of A b.
Diameter of A
Radius of B c.
Diameter of B d.
SOLUTION a.
The radius of A is 3 units. b.
The diameter of A is 6 units. c.
The radius of B is 2 units. d.
The diameter of B is 4 units.

10. EXAMPLE 3
Draw common tangents
Tell how many common tangents the circles have and draw them. a. b.
SOLUTION a.
4 common tangents
3 common tangents b.

11. EXAMPLE 3
Draw common tangents
Tell how many common tangents the circles have and draw them. c.
SOLUTION c.
2 common tangents

12. Assignment 1 of 2
#3-10 all, odd, page 655

14. 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.

15. 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.

17. 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.

18. Assignment 2 of 2
#19-25 odd, page 656