10.1 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Use Properties...
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Transcript of 10.1 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Use Properties...
10.1
Warm UpWarm Up
Lesson QuizLesson Quiz
Lesson PresentationLesson Presentation
Use Properties of Tangents
10.1 Warm-Up
1. What measure is needed to find the circumferenceor area of a circle?
2. Find the radius of a circle with diameter 8 centimeters.
ANSWER radius or diameter
ANSWER 4 cm
3. A right triangle has legs with lengths 5 inches and12 inches. Find the length of the hypotenuse.
ANSWER 13 in.
10.1 Warm-Up
4. Solve 6x + 15 = 33.
ANSWER 3
5. Solve (x + 18)2 = x2 + 242.
ANSWER 7
10.1 Example 1
Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of C.
ACa.
SOLUTION
is a radius because C is the center and A is a point on the circle.ACa.
b. AB
b. AB is a diameter because it is a chord that contains the center C.
10.1 Example 1
Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of C.
SOLUTION
c. DE is a tangent ray because it is contained in a line that intersects the circle at only one point.
DEc.
d. AE is a secant because it is a line that intersects the circle in two points.
AEd.
10.1 Guided Practice
1. In Example 1, what word best describes AG? CB?
ANSWER chord; radius
2. In Example 1, name a tangent and a tangent segment.
ANSWER DE, DB
10.1 Example 2
b. Diameter of A
Radius of Bc.
Diameter of Bd.
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.
10.1 Guided Practice
3. Use the diagram in Example 2 to find the radius and diameter of C and D.
ANSWER 3; 6; 2; 4
10.1 Example 3
Tell how many common tangents the circles have and draw them.
a.
SOLUTION
a. 4 common tangents
10.1 Example 3
Tell how many common tangents the circles have and draw them.
SOLUTION
b.
3 common tangentsb.
10.1 Example 3
Tell how many common tangents the circles have and draw them.
SOLUTION
c.
c. 2 common tangents
10.1 Guided Practice
Tell how many common tangents the circles have and draw them.
4.
2 common tangents
ANSWER
10.1 Guided Practice
Tell how many common tangents the circles have and draw them.
5.
1 common tangent
ANSWER
10.1 Guided Practice
Tell how many common tangents the circles have and draw them.
no common tangents
ANSWER
6.
10.1 Example 4
SOLUTION
Use the Converse of the Pythagorean Theorem. Because 122 + 352 = 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.
In the diagram, PT is a radius of P. Is ST tangent to P ?
10.1 Example 5
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
(r + 50)2 = r2 + 802
r2 + 100r + 2500 = r2 + 6400
100r = 3900
r = 39 ft
Pythagorean Theorem
Substitute.
Multiply.
Subtract from each side.
Divide each side by 100.
10.1 Example 6
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 .
10.1 Guided Practice
7. Is DE tangent to C?
ANSWER Yes
10.1 Guided Practice
ANSWER 7
8. ST is tangent to Q.Find the value of r.
10.1 Guided Practice
ANSWER ±3
9. Find the value(s) of x.
10.1 Lesson Quiz
ANSWER secant
1. Give the name that best describes the figure .
a. CD b. AB
c. FD d. EP
ANSWER tangent
ANSWER chord ANSWER radius
10.1 Lesson Quiz
ANSWER
One tangent; it is a vertical line through the point of tangency.
2. Tell how many common tangents the circles have .
10.1 Lesson Quiz
3. Is AB tangent to C? Explain. .
ANSWER
Yes; 16 + 30 = 1156 = 34 so AB AC, and a line to a radius at its endpoint is tangent to the circle.
2 22
10.1 Lesson Quiz
4. Find x.
ANSWER 12