MATHCP Geometry  - Unit 24: Special Segments and Equations of Circles
Review of the Quadratic Formula

In this unit, some problems involve quadratic equations that may be solved by using the quadratic formula. Thus, a short review of solving quadratic equations with real roots and applying the quadratic formula is given in the first four problems. Determine the POSITIVE value of “x” for each quadratic equation. Round the answers to the nearest tenth.

1) What is the positive value of “x”?

250 character(s) left

2) What is the positive value of “x”?

250 character(s) left

3) What is the positive value of “x”? (Hint: Write the equation in standard form.)

250 character(s) left

4) What is the positive value of “x”?

250 character(s) left

Chord, Secant, and Tangent Relationships

For the activity problems in this unit, measure the segments accurately to the nearest millimeter. Note: Even with accurate measurements, there may be a little variance; therefore, after each multiplication, round the answer to the nearest whole millimeter.

5) Activity: Print out the circle shown below and measure segments AE, BE, CE, and DE to the nearest millimeter. Multiply the length of AE times the length of EC. Multiply the length of BE times the length of ED. True or False: (AE)(EC) = (BE)(ED)

6) Activity: Print the circle shown below and measure segments FJ, GJ, HJ, and IJ to the nearest millimeter. Multiply the length of FJ times the length of JH. Multiply the length of GJ times the length of IJ. True or False: (FJ)(JH) = (GJ)(IJ)

7) Theorem 24-A: If two chords intersect in a circle, then the __________ of the measures of the segments are equal.

250 character(s) left

8) What is the length of CE if segments AE, BE, and DE measure 7 inches, 5, inches and 14 inches, respectively?

250 character(s) left

9) If VZ = 21, ZX = 24, and Z is the midpoint of WY, what is the length of WZ rounded to the nearest tenth?

250 character(s) left

10)

Answer the following questions about the figure and information given below: (a) What is the length of UP? (b) What expression may be used to represent the length of PT? (c) What expression may be used to represent RT? (d) What is the value of “x” rounded to the nearest tenth?

4000 character(s) left

11) Select the BEST term for the following description: “a line that intersects a circle in exactly two points”.

12) Select the BEST term for the following description: “a section of a secant line that lies in the area outside of a circle”.

13) Select the BEST term for the following description: “a section of a secant line that intersects a circle in exactly two points”.

Refer to the figure below to solve the next five problems.

14) Select the BEST term to describe the geometric name shown below.

15) Select the BEST term to describe the geometric name shown below.

16) Select the BEST term to describe the geometric name shown below.

17) Select the BEST term to describe the geometric name shown below.

18) Select the BEST term to describe the geometric name shown below.

19) Activity: Print out the circle shown below and measure segments TU, TV, TW, and TX to the nearest millimeter. Multiply the length of TU times the length of TV. Multiply the length of TW times the length of TX. True or False: (TU)(TV) = (TW)(TX)

20) Theorem 24-B: If two secant segments of a circle are drawn from an exterior point, then the product of the measures of one __________ __________ and its external secant segment is equal to the product of the measures of the other secant segment and its __________ segment.

250 character(s) left

21) Refer to the figure below to complete the following statement: (HE)(HD) = (HA)(?).

250 character(s) left

22) Theorem 24-C: If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the __________ of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external segment.

250 character(s) left

23) Refer to the figure below to complete the following statement: (HE)(HD) = (HB)(?).

250 character(s) left

24) Answer the following questions about the figure shown below: (a) What value is missing in the left side of the math statement? (b) What is the value of “x” rounded to the nearest tenth?

250 character(s) left

Refer to the figure and information given below to answer the next two questions.

25) Which of the statements shown below is the math statement that may be used to solve for “x” using the quadratic formula? State the letter of the correct answer.

250 character(s) left

26) What is the value of “x” rounded to the nearest tenth?

250 character(s) left

27) In the figure below, AB = 12, BC = 19, and ED = 14. What is the length of CD rounded to the nearest tenth?

250 character(s) left

28) In the figure below, if the length of AD is three times the length of CD, and BD = 15, (a) What is the length of CD? (b) What is the length of AD? (c) What is the length of AC? Round all answers to the nearest tenth.

4000 character(s) left

29) For the figure and information given below, what is the length of TU rounded to the nearest tenth?(Hint: Segments PQ, PS, and PU are radii of circle P.)

250 character(s) left

30) What is the length of HA in the figure below based on the given information? Explain the solution to the problem.

4000 character(s) left



Attachments
There are no attachments
 Attach a File
Equations and Graphs of Circles

In this section, follow the example shown below when asked to write the standard equation of a circle.

31) Use the distance formula and determine the standard equation for circle J with a radius of 6 and a center point J(–2, 3). State the letter of the correct answer.

250 character(s) left

32) Use the distance formula and determine the standard equation for circle M with a radius of 7 and a center point M(–5, –4).

250 character(s) left

33) The center of circle P in a coordinate plane and the length of its radius are shown below along with the general form for the standard equation of a circle. What is the standard equation of circle P? Simplify the equation, if necessary.

250 character(s) left

The chart below shows the centers of five circles in a coordinate plane and the length of their radii. Determine the standard equation of each circle and then answer the next five questions.

34) What is the standard equation for circle P?

250 character(s) left

35) What is the standard equation for circle Q?

250 character(s) left

36) What is the standard equation for circle R?

250 character(s) left

37) What is the standard equation for circle S?

250 character(s) left

38) What is the standard equation for circle T?

250 character(s) left

39) The standard equation of circle Q is given below along with the general form of the standard equation of a circle. What is the location of the center of circle Q in a coordinate plane and what is the length of its radius?

250 character(s) left

40) The standard equation of circle R is given below along with the general form of the standard equation of a circle. What is the location of the center of circle R in a coordinate plane and what is the length of its radius?

250 character(s) left

In the chart shown below, the name of five circles and their corresponding equations are given. For each circle, determine the coordinates of the center of the circle in a coordinate plane and the length of the radius. Complete the chart, and then answer the next five questions.

41) What is the location of the center of circle T? What is the circle’s radius?

250 character(s) left

42) What is the location of the center of circle U? What is the circle’s radius?

250 character(s) left

43) What is the location of the center of circle V? What is the circle’s radius?

250 character(s) left

44) What is the location of the center of circle W? What is the circle’s radius?

250 character(s) left

45) What is the location of the center of circle X? What is the circle’s radius?

250 character(s) left

46) In the figure below, segment ST is the diameter of the circle. (a) What is the location of the center of the circle? (b) What is the length of the radius of the circle? (c) What is the standard equation of the circle?

4000 character(s) left

Graphing Irrational Numbers

47) The graph below shows the approximate location of the square root (74) on the number line. (a) What number, when squared and added to the square of 7 (49), equals 74? (b) The square root (74) is located approximately where on the number line? (Round the answer to the nearest tenth.)

250 character(s) left

48) The method shown above illustrates that irrational numbers may be graphed on a number line. Which property listed below is NOT a property of irrational numbers?

49) Follow the given steps given below to create a circle from any three noncollinear points. Use a compass and straight edge. Describe your final drawing.

4000 character(s) left



Attachments
There are no attachments
 Attach a File
Extended Research: Check with your instructor to see if he/she is interested in awarding extra credit to you for writing a one-page report on the following research topic: Stonehenge is a site in England where huge stones were placed in a circle more than a thousand years ago. Do an Internet search and find some theories about the use of Stonehenge, who built it, and the mysteries of it. Write a one page paper about the history of Stonehenge. Include theories that illustrate that the ancient builders had knowledge of geometry.

50) If you were directed by your school to complete Offline Activities for this course, please enter the information on the Log Entry form.
No offline activities found
0 Hour(s) & 0 Minute(s)

If you are NOT required to complete Offline Activities for this course, please check the box below.



Attachments
There are no attachments
 Attach a File