Download presentation

Presentation is loading. Please wait.

Published byElle Farrand Modified over 7 years ago

1
Tangency

2
Lines of Circles

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 b. AB is a diameter because it is a chord that contains the center C. Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of C. b. AB SOLUTION

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

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

7
SOLUTION GUIDED PRACTICE for Example 1 Is a chord because it is a segment whose endpoints are on the circle. AG CB is a radius because C is the center and B is a point on the circle. 1. In Example 1, what word best describes AG ? CB ?

8
SOLUTION GUIDED PRACTICE for Example 1 2. In Example 1, name a tangent and a tangent segment. A tangent is DE A tangent segment is DB

9
EXAMPLE 2 Find lengths in circles in a coordinate plane b. Diameter of A Radius of B c. Diameter of B d. Use the diagram to find the given lengths. a.Radius of A 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
SOLUTION GUIDED PRACTICE for Example 2 a.The radius of C is 3 units. b.The diameter of C is 6 units. c. The radius of D is 2 units. d. The diameter of D is 4 units. 3. Use the diagram in Example 2 to find the radius and diameter of C and D.

11
Diagram Common tangents

12
EXAMPLE 3 Draw common tangents Tell how many common tangents the circles have and draw them. a.b. c. SOLUTION a. 4 common tangents 3 common tangents b.

13
EXAMPLE 3 Draw common tangents c. 2 common tangents Tell how many common tangents the circles have and draw them. c. SOLUTION

14
GUIDED PRACTICE for Example 3 Tell how many common tangents the circles have and draw them. 4. 2 common tangents

15
SOLUTION GUIDED PRACTICE for Example 3 Tell how many common tangents the circles have and draw them. 1 common tangent 5.

16
SOLUTION GUIDED PRACTICE for Example 3 Tell how many common tangents the circles have and draw them. No common tangents 6.

17
Theorem Tangent Perpendicular

18
Theorem Tangent Perpendicular Converse

19
EXAMPLE 4 Verify a tangent to a circle SOLUTION Use the Converse of the Pythagorean Theorem. Because 12 2 + 35 2 = 37 2, 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. In the diagram, PT is a radius of P. Is ST tangent to P ?

20
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. AC 2 = BC 2 + AB 2 (r + 50) 2 = r 2 + 80 2 r 2 + 100r + 2500 = r 2 + 6400 100r = 3900 r = 39 ft. Pythagorean Theorem Substitute. Multiply. Subtract from each side. Divide each side by 100.

21
Theorem Common Point Tangency

22
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 28 = 3x + 4 8 = x Substitute. Solve for x. Tangent segments from the same point are

23
GUIDED PRACTICE for Examples 4, 5 and 6 7. Is DE tangent to C ? ANSWER Yes

24
GUIDED PRACTICE for Examples 4, 5 and 6 8. ST is tangent to Q.Find the value of r. ANSWER r = 7

25
GUIDED PRACTICE for Examples 4, 5 and 6 9. Find the value(s) of x. + 3 = x ANSWER

Similar presentations

© 2023 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google