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Tenth Grade (Grade 10) Circles Questions

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Grade 10 Circles CCSS: HSG-C.A.4

Which line segment is tangent to circle O?

[math]bar(AB[/math]
[math]bar(AC[/math]
[math]bar(AD[/math]
[math]bar(AO[/math]

Grade 10 Circles

For each part of the circle listed below, choose ALL of the properties which are true about it.

	Always intersects the center of the circle	Touches only ONE point on the circle	Can form inscribed angles
Radius
Diameter
Tangent
Chord

Grade 10 Circles

What can you tell about segment AB?

If AB were a part of a line it could be called a secant segment.
AB is a line segment.
All of the above
None of the above

Grade 10 Circles

If chord AB passes through the center of the circle, what is its name?

the radius
the diameter
the chord
the line segment
the midline

Grade 10 Circles CCSS: HSG-C.A.2

If a diameter is drawn perpendicular to the chord shown on this circle, it will bisect the chord and the arcs it defines.

True
False

Grade 10 Circles

In circle O, which is the chord?

AB
OD
AC
AO

Grade 10 Circles

What is the name of this segment drawn on the circle?

diameter
half-diameter
radius
midline
chord

Grade 10 Circles CCSS: HSG-C.A.4

Line segment [math]bar{AC}[/math] is tangent to circle O.

True
False

Grade 10 Circles

The line drawn across this circle is a diameter. The two arcs defined by this line are called semicircles and their degree measure is 180 .

Grade 10 Circles CCSS: HSG-C.A.4

Line segments [math]bar{AB}[/math] and [math]bar{BC}[/math] are both tangent to the circle.

True
False

Grade 10 Circles

Given the circle below, and the fact that [math]bar{AD}[/math] passes through the center of the circle, what is the measure of [math]ang ADB[/math] if [math]m ang ABD = 25° ?[/math]

Not enough information
65°
90°
155°

Grade 10 Circles

If point A is equidistant from all of the points in the circle, what is point A called?

the midpoint
the focus
the center
the point
the middle

Grade 10 Circles

A line in the plane of a circle that intersects the circle in exactly one point.

perimeter
circumference
bisector
tangent

Grade 10 Circles

For the proof shown, choose the correct reasons for steps 4 and 6.

Given: The circle pictured with diameter [math]bar{AD}[/math] (not drawn), with [math]bar{AB}[/math] tangent to the circle, and line [math]bar{AC}[/math] also not drawn.
Prove: [math]triangle ABD \ ~ triangle CAD [/math].

Circle with Secant CD and Tangent AB

[math] " Statement " [/math]	[math] " Reason "[/math]
[math]1. "Draw " bar(AD) \ & \ bar{AC}[/math]	[math]1. "Two points create a line"[/math]
[math]2. bar(AD) \ \ "is a diameter"[/math]	[math]2. "Given"[/math]
[math]3. ang ACD \ \ "is a right angle"[/math]	[math]3. "Inscribed angle subtended by a diameter is a right angle"[/math]
[math]4. bar(AB) \ \ "is tangent to the circle"[/math]	[math]4.[/math]
[math]5. bar{AB} _\|_ bar{AD}[/math]	[math]5. "A tangent line is perpendicular to the diameter"[/math]
[math]6. ang BAD \ \ "is a right angle"[/math]	[math]6. [/math]
[math]7. ang ACD ~= ang BAD[/math]	[math]7. "All right angles are congruent"[/math]
[math]8. ang ADC ~= ang ADB[/math]	[math]8. "Reflexive property"[/math]
[math]9. triangle ABD \ ~ triangle CAD[/math]	[math]9. "AA"[/math]

Looks correct; Definition of perpendicular lines
Given; Triangle ABD is a right triangle
Definition of a Tangent; Looks correct
Given; Definition of perpendicular lines

Grade 10 Circles

Which is an inscribed angle?

[math]ang CAB[/math]
[math]ang ADO[/math]
[math]ang DAB[/math]
[math]ang BOD[/math]

Grade 10 Circles

What are the missing reasons in steps 2 and 6 for the proof?

Given the circle shown, where [math]m \stackrel{\frown}{EB} = m \stackrel{\frown}{DC}[/math] and with [math]bar{EC}, bar{BD}, & \ bar{ED}[/math] not drawn, prove that [math]triangle EBD ~= triangle DCE[/math].

Circle with Two Secants ABCDE

[math] " Statement " [/math]	[math] " Reason "[/math]
[math]1. "Draw " bar{EC}, bar{DB}, & \ bar{ED}[/math]	[math]1. "Two points define a line"[/math]
[math]2. m \stackrel{\frown}{EB} = m \stackrel{\frown}{DC}[/math]	[math]2. [/math]
[math]3. m ang EDB = 1/2 m \stackrel{\frown}{EB}[/math]	[math]3. "Measure of inscribed angle is 1/2 the measure of intercepted arc"[/math]
[math]4. m ang CED = 1/2 m \stackrel{\frown}{CD}[/math]	[math]4. "Measure of inscribed angle is 1/2 the measure of intercepted arc"[/math]
[math]5. 1/2 m \stackrel{\frown}{EB} = 1/2 m \stackrel{\frown}{DC}[/math]	[math]5. "Multiplicative Property of Equality"[/math]
[math]6. m ang EDB = m ang CED[/math]	[math]6. [/math]
[math]7. ang EDB ~= ang CED[/math]	[math]7. "Definition of congruent angles"[/math]
[math]8. ang EBD ~= ang ECD[/math]	[math]8. "Inscribed angles intercepting the same arc are congruent"[/math]
[math]9. bar{ED} ~= bar{ED}[/math]	[math]9. "Reflexive Property"[/math]
[math]10. triangle EBD ~= triangle DCE[/math]	[math]10. "AAS"[/math]

Given; Substitution Property of Equality
Assume from diagram; Closure Property of Addition
Given; Addition Property of Equality
Assume from diagram; Closure Property of Multiplication

Grade 10 Circles

What is the radius of a circle with a circumference of 56.52 m?

7 m
9 m
18 m
14 m

Grade 10 Circles

What are line segments AE and AD called?

Tangents
Secants
Cosecants
Diameters
Chords

Grade 10 Circles CCSS: HSG-C.A.1

This question is a part of a group with common instructions. View group »

If the two circles' radii are congruent, can the circles still be shown to be similar?

No, since they are congruent.
No, since there exists no scale factor that will dilate one circle onto the other.
Yes, since all congruent shapes are similar (with scale factor 1).
Yes, since congruent radii means they have the same area, and any shapes with equal areas are similar.

Grade 10 Circles CCSS: HSG-C.A.2

Chord AB is 5 inches from the center of the circle. The radius of the circle is 13 inches. What is the length of the chord? 24 inches

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Tenth Grade (Grade 10) Circles Questions