Student Name: Teacher: Date: District: Miami-Dade County Public Schools Assessment: 9_12 Mathematics Geometry Exam 3. Form: 201

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1 Student Name: Teacher: District: Date: Miami-Dade County Public Schools Assessment: 9_12 Mathematics Geometry Exam 3 Description: Geometry Topic 6: Circles Form: Which method is valid for proving that two circles are similar? MAFS.912.G-1.1 Calculate the ratio of the diameter to the radius for each circle and show that they are equal. Calculate the ratio of degrees to the circumference for each circle and show that they are equal. Calculate the ratio of the area to the circumference for each circle and show that they are equal. Calculate the ratio of the diameter to the circumference for each circle and show that they are equal. 2. The equation is the equation of a circle written in standard form. Which of the following equations is the same circle written in vertex form? MAFS.912.G-GPE.1.1

2 3. The circle below is the graph of which of the following equations? MAFS.912.G-GPE.1.1

3 4. Ashley is studying circle O, shown below. She wrote the steps below. What did Ashley derive? MAFS.912.G-2.5 that all circles are similar the formula for arc length the formula for the area of a sector of a circle that a central angle has the same measure as the arc it subtends

4 5. In these two constructions, is the diameter of Circle O. Which of these constructions is the best first step to construct a square inscribed in Circle O? MAC912.G-CO.4.13 only Construction 1 only Construction 2 both Construction 1 and Construction 2 neither Construction 1 nor Construction 2 6. Use the circle shown to answer the question. If and find the value of x. MAFS.912.G-1.2

5 7. Read the directions for a geometric construction. 1. Start with a circle with the center given. 2. Mark a point anywhere on the circle. 3. Place the compass needle on the created point and set the width of the compass to measure the distance between that point and the center of the circle. 4. Keep the compass needle on the point and draw an arc intersecting the circle. 5. Move the compass to the intersection of the circle and the arc and draw another arc intersecting the circle. 6. Continue until there are six points of intersection between the given circle and the constructed arcs. 7. Connect every other point of intersection. This construction will result in which type of geometric construction? MAFS.912.G-CO.4.13 a circle inscribed in an equilateral triangle an equilateral triangle inscribed in a circle a circle inscribed in a regular hexagon a regular hexagon inscribed in a circle 8. Which measurement is closest to the area of the shaded sector in the circle shown below? MAFS.912.G square inches square inches square inches square inches

6 9. In the given figure, is tangent to circle M at point If find the length of MAFS.912.G Quadrilateral ABCD is inscribed in Circle Z such that side is a diameter of Circle Z as shown below. If and what is MAFS.912.G

7 11. The figure below shows the circles and Which of these statements can be used to prove that the circles are similar? MAFS.912.G-1.1 The circles and are similar because can be mapped onto by a translation two units to the right and three units up followed by a dilation about its center by a scale factor of The circles and are similar because can be mapped onto by a translation two units to the right and three units up followed by a dilation about its center by a scale factor of 2. The circles and are similar because can be mapped onto by a translation two units to the left and three units down followed by a dilation about its center by a scale factor of The circles and are similar because can be mapped onto by a translation two units to the left and three units down followed by a dilation about its center by a scale factor of 2.

8 12. James wants to construct a regular hexagon inscribed in a circle with center O and diameter PQ. Which of these would be the next step of construction? MAFS.912.G-CO.4.13 Place the compass at O and draw an arc of length OP across the circle. Place the compass at P and draw an arc of length OP across the circle. Place the compass at Q and draw an arc of length QP across the circle. Place the compass at P and draw an arc of length PQ across the circle.

9 13. The students in a geometry class use the area of a parallelogram to informally determine the formula for the area of a circle. Their steps are as shown below. Step 1: Divide a circle into 12 wedges of equal size. Step 2: Rearrange the wedges alternately up and down to resemble the shape of a parallelogram. Step 3: Determine the dimensions of the parallelogram. The height, h, of the parallelogram approximates the radius, r, of the circle. What part of the circle is approximated by the base of the parallelogram? MAFS.912.G-GM1.1 one-sixth of the circumference one-half of the circumference the circumference twice the circumference

10 14. In the figure below, Circle C has tangent lines and and diameter Angle QSR measures What is the measure of MAFS.912.G-1.2

11 15. Paul designed a reverse curve section of a circular model train track as shown below. What is the approximate length, in inches, of the reverse curve section? MAFS.912.G

12 16. In circle M below, What is the measure of MAFS.912.G-1.2

13 17. Which construction will result in Circle P being inscribed in MAFS.912.G-1.3

14 18. Circle D is inscribed in, as shown below. What is the perimeter of MAFS.912.G If is the radian measure of a central angle of a circle and r is the radius of the circle, which is the correct derivation of the area, A, of the sector bounded by the sides of the central angle and the arc it subtends? MAFS.912.G-2.5

15 20. A circle of radius r is divided into n equal sections. In the figure below, The area of the circle can be estimated by thinking of each pie-shaped piece as a triangle with base b and height h. The more sections (n) the circle is divided into, the closer the approximation of the area. As n gets larger, which statements must be true? MAFS.912.G-GM1.1 Webb: What is the center and radius of the circle given by the equation: x 2 + y 2-4x + 2y - 4 = 0? MAFS.912.G-GPE.1.1 center: (-2, 1), r = 3 center: (2, -1), r = 3 center: (-2, 1), r = 9 center: (2, -1), r = 9

16 22. Which of these points lies on the circle that is centered at and passes through the point MAFS.912.G-GPE Carlos states that all circles can be proven to be similar by comparing the ratio of the diameter to the circumference of each circle. Monica disagrees and states that comparing the ratios of the radius to the circumference of each circle is the only way to prove that all circles are similar. Which statement is true? MAFS.912.G-1.1 Both Carlos and Monica are correct because either method is sufficient to prove two circles are similar. Both Carlos and Monica are incorrect because neither method is sufficient to prove two circles are similar. Monica is correct because comparing the ratios of radius to circumference is the only way to prove two circles are similar. Carlos is correct because comparing the ratios of diameter to circumference is the only way to prove two circles are similar. 24. Which statement is valid when a circumscribed circle of an obtuse triangle is constructed? MAFS.912.G-1.3 The longest side of the triangle lies on the diameter of the circle. The circle is drawn inside the triangle touching all 3 sides. The center of the circle is in the interior of the triangle. The vertices of the triangle lie on the circle.

17 25. What is the equation of a circle with radius, and the center at MAFS.912.G-GPE In Circle A, segments and are tangents to the circle at B and D, respectively. Angle BGD is an inscribed angle with a measurement of Which expression shows the relationship between MAFS.912.G-1.2

18 27. Circle P has a radius of units. It includes a sector with a central angle of and an area of 1 square unit. Which proportion could be used to determine the value of x? MAFS.912.G A diameter of Circle P has endpoints Which point also lies on Circle P? MAFS.912.G-GPE.2.4 (3, 3)

19 29. Jeremiah wants to construct an equilateral triangle inscribed in a circle using a straightedge and a compass. Which set of markings best reflects Jeremiah s work to complete the desired construction? MAFS.912.G-CO.4.13

20 30. In the figure below, are radii of the circle with center O. Given that what is MAFS.912.G

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