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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?
Circle ABCD
  1. ¯AB
  2. ¯AC
  3. ¯AD
  4. ¯AO
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?
Circle with Chord AB
  1. If AB were a part of a line it could be called a secant segment.
  2. AB is a line segment.
  3. All of the above
  4. None of the above
Grade 10 Circles
If chord AB passes through the center of the circle, what is its name?
Circle with Diameter AB
  1. the radius
  2. the diameter
  3. the chord
  4. the line segment
  5. the midline
Grade 10 Circles
In circle O, which is the chord?
Circle ABCD
  1. AB
  2. OD
  3. AC
  4. AO
Grade 10 Circles
What is the name of this segment drawn on the circle?
Circle with Radius
  1. diameter
  2. half-diameter
  3. radius
  4. midline
  5. chord
Grade 10 Circles
If point A is equidistant from all of the points in the circle, what is point A called?
Circle with Center Point A
  1. the midpoint
  2. the focus
  3. the center
  4. the point
  5. the middle
Grade 10 Circles
A line in the plane of a circle that intersects the circle in exactly one point.
  1. perimeter
  2. circumference
  3. bisector
  4. tangent
Grade 10 Circles
Which is an inscribed angle?
Circle ABCD
  1. ∠CAB
  2. ∠ADO
  3. ∠DAB
  4. ∠BOD
Grade 10 Circles
What are the missing reasons in steps 2 and 6 for the proof?

Given the circle shown, where m⌢EB=m⌢DC and with ¯EC,¯BD,& ¯ED not drawn, prove that △EBD≅△DCE.

Circle with Two Secants ABCDE

Statement Reason
1.Draw ¯EC,¯DB,& ¯ED1.Two points define a line
2.m⌢EB=m⌢DC2.
3.m∠EDB=12m⌢EB3.Measure of inscribed angle is 1/2 the measure of intercepted arc
4.m∠CED=12m⌢CD4.Measure of inscribed angle is 1/2 the measure of intercepted arc
5.12m⌢EB=12m⌢DC5.Multiplicative Property of Equality
6.m∠EDB=m∠CED6.
7.∠EDB≅∠CED7.Definition of congruent angles
8.∠EBD≅∠ECD8.Inscribed angles intercepting the same arc are congruent
9.¯ED≅¯ED9.Reflexive Property
10.△EBD≅△DCE10.AAS
  1. Given; Substitution Property of Equality
  2. Assume from diagram; Closure Property of Addition
  3. Given; Addition Property of Equality
  4. Assume from diagram; Closure Property of Multiplication
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?
  1. No, since they are congruent.
  2. No, since there exists no scale factor that will dilate one circle onto the other.
  3. Yes, since all congruent shapes are similar (with scale factor 1).
  4. Yes, since congruent radii means they have the same area, and any shapes with equal areas are similar.
Grade 10 Circles
What are line segments AE and AD called?
Circle with Two Secants ABCDE
  1. Tangents
  2. Secants
  3. Cosecants
  4. Diameters
  5. Chords
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