University:
College Entrance Preparation
Course:
ACT Preparation (Mathematics)
Academic year:

2024
Views:

316

Pages:

4
Author:

Nicole Wang

CHAPTER 6: CIRCLES! CLASSWORK Day # 25 OBJECTIVE: 6.2 Tangent Properties Date: 5-8-13 VOCABULARY Tangent circles Circles that are tangent to the same line at the same point. Internally tangent Tangent circles that are inside one another. Externally tangent Tangent circles that are not inside one another. 1. Tangent Conjecture 2. Tangent Segments A tangent to a circle is Tangent segments to a circle from a perpendicular to the radius point outside the circle are drawn to the point of tangency. congruent. 1. Rays r and s are tangents; w = 126° [Image of two circles with tangent lines, labeled with angles] 180 54 234 234 126 2. AB is tangent to both circles and m∠MC = 295°, m∠BOX = 65° [Image of two intersecting circles with tangent line AB and labeled angles] 295° M B 15° 65° C X Q 3. PQ is tangent to two externally tangent noncongruent circles, M and N. a. What kind of quadrilateral is MNQP? Explain your reasoning. [Image of two externally tangent circles with a tangent line PQ] Trapezoid b. If circles M and N are congruent, what is MNQP? Explain why. Parallelogram 4. AT is tangent to circle P. Find the equation of AT. [Image of a circle P with a tangent line AT and labeled points] (3,9) y = mx + b m AP = 9/3 = 3 y - y₁ = m(x - x₁) y - 9 = 3(x - 3) y - 9 = 3x - 9 y = 3x + 10 Tangent circles are two circles that are tangent to the same line at the same point. They can be internally tangent or externally tangent, as shown. HW#21 Externally tangent circles Internally tangent circles EXERCISES 1. Rays m and in are tangent to circle P. w 2 Raysands are tangent to circle Qx1 55 Q 180 -130 50 130 50° 3. Ray k is tangent to circle R. 30 4. Line t is tangent to both circles. 2=105° 75 M 180 -15 105 20 You will need Construction tools for Exercises 8-12 and 15 Geometry software for Exercises 13 and 26 180 -70 110-2-55 5. Quadrilateral POST is circumscribed about circle Y. OR 13 and ST 12. What is the perimeter of POST? 13 130 13 C 6 Y 13 R 6 376 66 Pam participates in the hammer-throw event. She swings a 16 lb ball at arm's length, about eye-level. Then she releases the ball at the precise moment when the ball will travel in a straight line toward the target area. Draw an overhead view that shows the ball's circular path, her arms at the moment she releases it, and the ball's straight path toward the target area. Explain how you could use only a T-square, like the one shown, to find the center of a Frisbee. Parn Dukes competes in the hammer-throw event. LESSON 6.2. Tangent Properties 315