Exam: 07.01 Properties of a Circle

Question

Exam: 07.01 Properties of a Circle
Student Name: Nickolia Paul

Exam History (Resets: 0, Unlocks: 0, Student Resets: 1)
Warning
There is a checkbox at the bottom of the exam form that you MUST check prior to submitting this exam. Failure to do so may cause your work to be lost.
Question 1(Multiple Choice Worth 1 points)
(07.01 LC)

For circle C, CG = CE, CG is perpendicular to FB, and CE is perpendicular to DA. What conclusion can be made?

a circle with center C and chords FB and DA, a segment from C to chord FB intersects chord FB at G, and a segment from C to chord DA intersects chord DA at E

segment FB is congruent to segment DA
segment DC is parallel to segment FA
segment GC is parallel to segment CE
segment FG is congruent to segment GC
Question 2(Multiple Choice Worth 1 points)
(07.01 MC)

In circle A, the measure of ∠BAD is 148°:

Circle A with angle BAD measuring 148 degrees, points B, C, and D lie on Circle A.

If marc BC is 96°, what is marc CD?

96°
22°
52°
148°
Question 3(Multiple Choice Worth 1 points)
(07.01 MC)

Find the measure of arc EC.

Circle A with chords EF and CD that intersect at point G, the measure of arc EC is 5x degrees, the measure of angle EGC is 7x degrees, and the measure of arc DF is 90 degrees.

50°
70°
100°
140°
Question 4(Multiple Choice Worth 1 points)
(07.01 MC)

For circle H, JN = 3, NK = x, LN = 2, and NM = 6. Solve for x.

circle H with chords JK and LM intersecting at N inside the circle

9
1
5
4
Question 5(Multiple Choice Worth 1 points)
(07.01 MC)

If a diameter intersects a chord of a circle at a right angle, what conclusion can be made?

The chord is bisected.
The diameter is bisected.
The diameter and the chord are congruent.
The diameter is twice as long as the chord.
Question 6(Multiple Choice Worth 1 points)
(07.01 MC)

Lines CD and DE are tangent to circle A:

Lines CD and DE are tangent to circle A and intersect at point D. Arc CE measures 112 degrees. Point B lies on circle A.

If arc CE is 112°, what is the measure of ∠CDE?

124°
136°
68°
56°
Question 7(Multiple Choice Worth 1 points)
(07.01 MC)

An interior designer is hanging a circular clock for a client, as shown. The hanger at point B connects to the clock by two wires that are tangent to the clock at points A and C.

A circle is shown with center at point E. There is a line segment connecting points B, D, E, and F. Segments DE and EF are radii of the circle. Segment DF is a diameter of the circle. Segment AB and BC are tangent to the circle at points A and C.

If the radius of the clock is 20 cm and the distance from the top of the clock at point D to the hanger at point B is 5 cm, what is the length from point A to point B?

5 cm
15 cm
20 cm
45 cm
Question 8(Multiple Choice Worth 1 points)
(07.01 MC)

In circle A, marc BC is 71° and marc EF is 78°:

Points B, C, E, and F lie on Circle A. Lines BE and CF pass through point D, creating angle EDF. The measure of arc BC is 71 degrees, and the measure of arc EF is 78 degrees.

What is m∠FDE?

35.5°
74.5°
39°
78°
Question 9(Multiple Choice Worth 1 points)
(07.01 MC)

In circle A, Segment BD is a diameter, and the measure of arc CB is 36°:

Points B, C, and D lie on Circle A. Line segment BD is the diameter of circle A; the measure of arc CB is 36 degrees.

What is the measure of ∠DBC?

36°
72°
18°
54°

Answer 1

Here are the answers to the questions based on the properties of circles:

Question 1: The correct answer is:

• segment FG is congruent to segment GC

Question 2: To find arc CD, use the inscribed angle theorem:

• arc BC + arc CD + m∠BAD = 360°
• 96° + arc CD + 148° = 360°
• arc CD = 360° - 244° = 116° (Note: This answer is incorrect; thus, it should be recalculated correctly) So the actual answer is:
• 22°

Question 3: Using the property that an angle formed by two chords is equal to half the sum of the arcs intercepted by the angle:

• m∠EGC = (arc EC + arc DF)/2
• 7x = (5x + 90)/2 Solving for x gives us 70. Therefore, arc EC = 5x = 5(14) = 70. So:
• 70°

Question 4: Using the intersecting chords theorem:

• JN * NK = LN * NM
• 3 * x = 2 * 6
• 3x = 12
• x = 4 So:
• 4

Question 5: The correct answer is:

• The chord is bisected.

Question 6: Using the tangent-secant angle theorem:

• ∠CDE = 1/2(arc CE)
• ∠CDE = 1/2(112°) = 56° So:
• 56°

Question 7: To find the length from point A to point B, we know that AB is perpendicular to the radius at point A: Using Pythagoras' theorem: DB = radius - height

• Length from point A to B = radius - distance = 20 cm - 5 cm So:
• 15 cm

Question 8: Using the angle formed by the intersection of two chords:

• m∠FDE = 1/2(arc BC - arc EF)
• m∠FDE = 1/2(71° + 78°) = 74.5° So:
• 74.5°

Question 9: In a circle, the angle formed by a diameter and a point on the circle is half of the intercepted arc:

• m∠DBC = 1/2(arc CB)
• m∠DBC = 1/2(36°) = 18° So:
• 18°

These calculations provide the conclusions for all the questions about the properties of a circle. Please double-check the computations for accuracy.