theorem 3: theorem 4
Post on 04-Jan-2022
15 Views
Preview:
TRANSCRIPT
Name: ______________________________________________________________ Date: ______________________ Period: ______
Chapter 14: Circle Segment Relationships Topic 3: Segments Theorems - Tangents
Theorem 3: If a line is tangent to a circle,
it is perpendicular to the radius drawn to ๐ผ๐น: ๐ด๐ตฬ ฬ ฬ ฬ is a tangent the point of tangency. ๐ท is a point of tangency ๐๐ป๐ธ๐: ๐๐ทฬ ฬ ฬ ฬ โฅ ๐ด๐ตฬ ฬ ฬ ฬ
Theorem 4: Tangent segments to a circle from the same external point are congruent.
IF: ๐ด๐ตฬ ฬ ฬ ฬ is tangent to circle ๐ at ๐ด ๐ถ๐ตฬ ฬ ฬ ฬ is tangent to circle ๐ at ๐ถ
Then: ๐ด๐ตฬ ฬ ฬ ฬ โ ๐ถ๐ตฬ ฬ ฬ ฬ Practice: 1.) ๐ถ๐ตฬ ฬ ฬ ฬ is a tangent. Find x. 2.) ๐ถ๐ตฬ ฬ ฬ ฬ is a tangent. Find x. 3.) In the diagram, is ๐ถ๐ตฬ ฬ ฬ ฬ a tangent? 4.) ๐ด๐ถฬ ฬ ฬ ฬ is a diameter, the radius = 9, ๐ถ๐ตฬ ฬ ฬ ฬ = 24, ๐ด๐ตฬ ฬ ฬ ฬ = 30. Is ๐ถ๐ตฬ ฬ ฬ ฬ a tangent?
5.) ๐ด๐ตฬ ฬ ฬ ฬ , ๐ถ๐ตฬ ฬ ฬ ฬ are tangents. Find x. 6.) ๐ด๐ตฬ ฬ ฬ ฬ , ๐ถ๐ตฬ ฬ ฬ ฬ are tangents. Find x. 7.) Find the perimeter of โ๐ด๐ต๐ถ 8.) Find the perimeter of โ๐ด๐ต๐ถ Common Core Questions: 9.) In circle A, the radius is 9 mm and BC = 12 mm. (a) Find AC. (b) Find the area of โ๐ด๐ถ๐ท. (c) Find the perimeter of quadrilateral ABCD.
10.) In circle A, EF = 12 and AE = 13. AE:AC = 1:3. (a) Find the radius of the circle. (b) Find BC (round to the nearest whole number). (c) Find EC.
11.) ๐ต๐ถฬ ฬ ฬ ฬ is tangent to circle A at point B. DC = 9 and BC = 15. (a) Find the radius (r) of the circle. (b) Find AC.
12.) In the diagram, what do you think the length of z could be? How do you know? 13.) In the figure given, the three segments are tangent to the circle at points F, B, and G. Find DE. Explain how you arrived at your answer.
Name: ______________________________________________________________ Date: ______________________ Period: ______
Segments Theorems - Tangents HOMEWORK
Complete the following questions below. Show all work, including formulas.
1.) In the diagram below, circles X and Y have two tangents drawn to them from external point T. The points of tangency are C, A, S, and E. The ratio of TA to AC is 1:3. If TS = 24, find the length of SE. 2.) Mrs. Smith wants to purchase a cover for their new circular pool. She needs to know the radius of the pool, but she does not want to get wet to take the measurements. She is standing 4 feet from the pool and 12 feet from the point of tangency. Find the radius of the pool. 3.) In the diagram below, ๐ด๐ตฬ ฬ ฬ ฬ , ๐ต๐ถฬ ฬ ฬ ฬ , and ๐ด๐ถฬ ฬ ฬ ฬ are tangents to circle O at points F, E, and D, respectively, AF = 6, CD = 5, and BE = 4. What is the perimeter of ฮABC? (1) 15 (2) 25
(3) 30 (4) 60 4.) As shown in the diagram below, ๐ต๐ฬ ฬ ฬ ฬ and tangents ๐ต๐ดฬ ฬ ฬ ฬ and ๐ต๐ถฬ ฬ ฬ ฬ are drawn from an external point B to circle O.
Radii ๐๐ดฬ ฬ ฬ ฬ and ๐๐ถฬ ฬ ฬ ฬ are drawn. If OA = 7 and DB = 18, determine and state the length of ๐ด๐ตฬ ฬ ฬ ฬ .
5.) The radius of circle A is 4. ๐ท๐ถฬ ฬ ฬ ฬ and ๐ถ๐ธฬ ฬ ฬ ฬ are tangent to the circle with DC = 12. (a) Find the length of ๐ด๐ต๐ถฬ ฬ ฬ ฬ ฬ ฬ in simplest radical form. (b) Find the area of quadrilateral ADCE to the nearest hundredth.
6.) In the diagram below, ๐ด๐ถฬ ฬ ฬ ฬ and ๐ต๐ถฬ ฬ ฬ ฬ are tangent to circle O at A and B, respectively, from external point C. If ๐โ ๐ด๐ถ๐ต = 38, what is ๐โ ๐ด๐๐ต? (1) 71 (2) 104 (3) 142 (4) 161 7.) In the diagram below, ๐ด๐ถฬ ฬ ฬ ฬ and ๐ด๐ทฬ ฬ ฬ ฬ are tangent to circle B at points C and D, respectively, and ๐ต๐ถฬ ฬ ฬ ฬ , ๐ต๐ทฬ ฬ ฬ ฬ , and ๐ต๐ดฬ ฬ ฬ ฬ are drawn. (a) If AC = 12 and AB = 15, what is the length of ๐ต๐ทฬ ฬ ฬ ฬ ? (b) What is the perimeter of quadrilateral ACBD?
Review Questions: 8.) Triangle ABC had vertices A(0,0), B(6,8), and C(8,4). Which equation represents the perpendicular bisector of ๐ต๐ถฬ ฬ ฬ ฬ ?
(1) y = 2x โ 6 (2) y = -2x + 4 (3) ๐ฆ =1
2๐ฅ +
5
2 (4) ๐ฆ = โ
1
2๐ฅ +
19
2
9.) A student used a compass and a straightedge to construct ๐ถ๐ธฬ ฬ ฬ ฬ in โ๐ด๐ต๐ถ as shown below. Which statement must always be true for this construction? (1) โ ๐ถ๐ธ๐ด โ โ ๐ถ๐ธ๐ต (2) โ ๐ด๐ถ๐ธ โ โ ๐ต๐ถ๐ธ (3) ๐ด๐ธฬ ฬ ฬ ฬ โ ๐ต๐ธฬ ฬ ฬ ฬ
(4) ๐ธ๐ถฬ ฬ ฬ ฬ โ ๐ด๐ถฬ ฬ ฬ ฬ 10.) Quadrilateral ABCD is graphed on the set of axes below. Classify quadrilateral ABCD. Explain your reasoning.
top related