Chapter 10-5 Tangents.

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Presentation transcript:

Chapter 10-5 Tangents

Use properties of tangents. tangent Solve problems involving circumscribed polygons. point of tangency Standard 7.0 Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles. (Key) Standard 21.0 Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles. (Key) Lesson 5 MI/Vocab

Reminder Tangent—a line that intersects the circle in only one point

Secant Tangent Diameter Radius Point of Tangency Chord

Tangent Theorem A line is tangent to a circle  it is  to a radius at its endpoint on the circle

Examples:

Find Lengths Because y is the length of the diameter, ignore the negative result. Thus, y is twice QR or y = 2(12) = 24. Lesson 5 Ex1

A. 15 B. 20 C. 10 D. 5 A B C D Lesson 5 CYP1

Identify Tangents Because the converse of the Pythagorean Theorem did not prove true in this case, ΔABC is not a right triangle. Lesson 5 Ex2

Identify Tangents First determine whether ΔEWD is a right triangle by using the converse of the Pythagorean Theorem. Because the converse of the Pythagorean Theorem is true, ΔEWD is a right triangle and EWD is a right angle. Lesson 5 Ex2

A. yes B. no C. cannot be determined A B C Lesson 5 CYP2

A. yes B. no C. cannot be determined A B C Lesson 5 CYP2

12 r r 10 r2 + 122 = (r + 10)2 r2 + 144 = r2 + 20r + 100 144 = 20r + 100 44 = 20r r =

If two segments from the same external point are tangent to a circle  they are  AC = AB A B C

Congruent Tangents ALGEBRA Find x. Assume that segments that appear tangent to circles are tangent. Lesson 5 Ex3

Use the value of y to find x. Congruent Tangents Use the value of y to find x. 10 Answer: 1 Lesson 5 Ex3

ALGEBRA Find a. Assume that segments that appear tangent to circles are tangent. Lesson 5 CYP3

Interactive Lab: Tangents and Communication Signals Triangles Circumscribed About a Circle Interactive Lab: Tangents and Communication Signals 16 45 16 + 29 = 45 18 P = 16 + 18 + 18 + 45 + 45 + 16 = 158 Lesson 5 Ex4

A. 86 B. 180 C. 172 D. 162 A B C D Lesson 5 CYP4

Common External Tangent Common Internal Tangent

Homework Ch 10-5 Pg 593 5 – 22, 30, 31, 43 – 46