Post Test: Circles

Select the correct answer. Which point lies on the circle represented by the equation (x − 3)^2 + (y + 4)^2 = 6^2 ?

(-3, -4)

Drag the tiles to the correct boxes to complete the pairs. Match each quadratic function to its graph.

(I don't know if yours is in the same order as mine so I'll describe the graph a little) Function facing upwards, above the x line and to the left of the y line = f(x) = 2(x + 3)^2 + 1 Function facing downwards, that is touching the x line and to the left of the y line = f(x) = -2(x + 3)^2 + 1 Function facing upwards, above the x line and to the right of the y line = f(x) = 2(x - 3)^2 + 1 Function facing downwards, below the x line and to the left of the y line = f(x) = -2(x + 3)^2 - 1

Which graph correctly represents the relationship between arc length and the measure of the corresponding central angle on a circle with radius r?

(It is C for me but I will describe it just in case) It's the graph with a straight line going upwards (not curved). Its lower numbers say (pie)/2, (pie), 3(pie)/2, and 2(pie).

Select the correct answer. Ali has a compass and a straightedge, and he wants to construct a square inscribed in a circle. Which figure shows the arcs he must draw to construct the square?

(It is D for me but I will describe it just in case) It is a circle with a horizontal line through the middle and a dot there as well. There are also one of each of of these )( intersecting (NOT TOUCHING... they are crisscrossed like an x) in the middle with the dot between.

Select the correct answer. Circle C has a center at (-2,10) and contains the point P(10,5). Which equation represents circle C?

(x + 2)^2 + (y - 10)^2 = 169

Select the correct answer. Which equation represents a circle with a center at (-5,5) and a radius of 3 units?

(x + 5)^2 + (y - 5)^2 = 9

What is the difference of the lengths of BD and CE ? Use the value (pie) = 3.14, and round the answer to two decimal places.

1.57 units

In the given circle, tangent AB and secant CD intersect at point E as shown. What is the value represented by x?

140

Select the correct answer. Arc CD located on circle A has a central angle of 135∘ . The radius of the circle is 24 centimeters. What is the length of arc CD ?

18(pie) cm

What is the ratio of the area of sector ABC to the area of sector DBE?

4/3

Select the correct answer. A rotating sprinkler head sprays water as far as 20 feet. The head is set to cover a central angle of 80∘ . What area of grass will be watered?

800/9 (pie) ft^2

Quadrilateral ABCD is inscribed in a circle. m∠A is 64°, m∠B is (6x + 4)°, and m∠C is (9x − 1)°. What is m∠D?

98 degrees

Type the correct answer in the box. Use numerals instead of words. A circular pool has a diameter of 30 feet. A section of the top railing with a central angle of 27∘ is broken and needs to be replaced. What approximate length of railing needs to be replaced? Round your answer to one decimal place.

About 7.1 feet of railing needs to be replaced.

Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Points C and D divide the semicircle into three equal parts. Match the angles with their measures.

CAE = 120 BAE = 180 DEC = 30 CAD = 60

Select the correct answer. Mel is teaching Travis how to use a compass and a straightedge to construct a square inscribed in a circle. He tells Travis to begin by using a straightedge to draw any chord of the circle and label it WX. Next, his instructions are to use the tools to construct a chord that is a perpendicular bisector of WX and label it YZ. Finally, he directs Travis to use a straightedge to draw the four chords that make up the square: WY, YX, XZ, and ZW. What is the first error, if any, Mel made in his instructions to Travis?

Chord WX must be a diameter of the circle.

Drag each tile to the correct box. The given steps for constructing a line tangent to circle O that is tangent to the circle at point P on the circle are listed out of order. Arrange the steps in the correct sequence. A. Without changing the compass width, place the compass on R and make another arc, intersecting the first, and label the intersection S. B. Draw a line through P and S. C. With the compass on P, draw an arc on each side of P. Label the intersections Q and R. D. Draw a straight line from the center, O, through P and extending past P. E. With the compass on Q, set its width to a setting greater than PQ. Make an arc outside the circle.

D, C, E, A, B (from left to right)

Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. With reference to the figure, match the angles and arcs to their measures.

DFA = 58 EOB = 122 COB = 114 CE = 124

Select the correct answer. Dylan constructed this figure using a compass with its width set equal to AX, the radius of the circle. He claims that the measures of the three sides of triangle ABX are all equal to AX, making ΔABX equilateral. Since this makes central angle AXB measure 60°, m AB = 60°. Dylan also claims that by repeatedly applying the same argument, he can prove that the inscribed hexagon is regular. Which statement is true?

Dylan's reasoning about arc AB is correct, and the hexagon is regular.

Select the correct answer. Casey constructed this figure by using a compass and a straightedge to draw circle O and diameter PQ. She then used a compass to draw two arcs. She labeled the points where those arcs intersect the circle M and N, and she drew the chords that form the triangle. If ΔMNP is equilateral, how did Casey draw the arcs that defined points M and N?

HERE IS WHAT IT IS NOT: She used a compass centered at P with a radius set equal to 3/4(PQ). AND She used a compass centered at O with a radius set equal to PO

Select the correct answer from each drop-down menu. A parabola is given by the equation y2 = -24x.

The equation of the directrix of the parabola is x = 6. The focus of the parabola is (-6, 0).

Type the correct answer in each box. The general form of the equation of a circle is x2 + y2 + 8x + 22y + 37 = 0.

The equation of this circle in standard form is (x + 4)^2 + (y + 11)^2 = 100. The center of the circle is at the point (-4, -11)

Type the correct answer in each box. Use numerals instead of words. Consider the given circle with the shaded sector XY and central angle, 225°. The circumference of the circle is 30(pie) units. Use the given information to complete the statements. Round any non-integer answers to the hundredths place.

The length of major arc XY is 58.9 units. The radius of the circle is 15 units. The area of the shaded sector is 441.79 square units.

Select the correct answer. In the given figure, m BC = 118, m BE = 76, and m BAC = 35. Which statement is true?

The measure of DE is 48, and triangle BCD is isosceles.

Type the correct answer in the box. Use numerals instead of words. An arc of circle M has length 32⁢(pie) centimeters and the corresponding central angle has a radian measure of 8/9 (pie) . What is the radius of the circle?

The radius of the circle is 36 centimeters.

Select the correct answer from each drop-down menu. Consider the circle with chords PR and QS intersecting at point T. Describe the relationship of the given segments. Then use the information to answer the following questions.

The segments can be related using the equation (PT)(TR) = (ST)(TQ) Using this relationship, the value of a is 6. Find the measure of ∠PTS by multiplying the sum of arcs PS and RQ by 1/2

When circle P is plotted on a coordinate plane, the equation of the diameter that passes through point Q on the circle is y = 4x + 2. Which statement describes the equation of a line that is tangent to circle P at point Q?

The slope of the tangent line is -1/4

Vance wants to construct a circle tangent to all three sides of the acute, scalene triangle LMN using the following steps. He will draw altitudes from vertex L and vertex M, and mark their intersection point as O. He will draw the perpendicular from point O to side MN, and mark the intersection point as P. He will draw the circle centered at point O which will pass through point P. Which part of Vance's plan requires revision?

Vance should have found the intersection of two angle bisectors of triangle LMN instead of two altitudes.

Josephine is constructing a circle circumscribed about triangle XYZ. She uses the following sequence of steps to construct the circle. She constructs the perpendicular bisectors of two sides. She finds their point of intersection, P. She uses a compass, with the fixed end on X, to draw a circle passing through point P. Did Josephine make any errors while constructing the circle?

Yes, she should have placed the compass with the fixed end on P and drawn a circle through point X.

Select the correct answer. What is the equation of the parabola opening upward with a focus at (9,27) and a directrix of y=11 ?

f(x) = 1/32 (x - 9)^2 + 19

Drag each tile to the correct box. Triangle ABC is inscribed in a circle centered at point O. Order the measures of the three intercepted arcs from least to greatest.

m AC < m BC < m AB

Points A and B are the endpoints of an arc of a circle. Chords are drawn from the two endpoints to a third point, C, on the circle. Given m AB = 64 and ABC = 73,

m ACB = 32 AND m AC = 146

Select the correct answer. Given the focus (-1, 15) and the directrix x = -4 , what is the equation of the parabola?

x = 1/6 (y - 15)^2 - 5/2