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Tenth Grade (Grade 10) Circles Questions

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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 CCSS: HSG-C.A.4
Which line segment is tangent to circle O?
Circle ABCD
  1. [math]bar(AB[/math]
  2. [math]bar(AC[/math]
  3. [math]bar(AD[/math]
  4. [math]bar(AO[/math]
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
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
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 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
Which is an inscribed angle?
Circle ABCD
  1. [math]ang CAB[/math]
  2. [math]ang ADO[/math]
  3. [math]ang DAB[/math]
  4. [math]ang BOD[/math]
Grade 10 Circles
Grade 10 Circles
Grade 10 Circles

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

Given the work in steps B - H to show that two circles are similar, could we use this to show that any two spheres are similar? If so, what needs to be changed or added?
  1. No, this is not possible.
  2. Yes, by starting with spheres, and projecting them onto the xy-plane, we can then follow the steps already established.
  3. Yes, but we would need to perform completely different transformations since we are now working in three dimensions.
  4. Yes, start with spheres instead of circles and then follow nearly identical steps.
Grade 10 Circles CCSS: HSG-C.A.1

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

If circle B's radius is larger that circle A's radius, what must change in our work to show that the two circles are similar?
  1. Nothing needs to change.
  2. They cannot be similar in this case.
  3. Circle A must be translated to circle B.
  4. The dilation scale factor must change.
Grade 10 Circles CCSS: HSG-C.A.1

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

After increasing the radius of circle B, such that it is equal to the radius of circle A, how can we be sure that the two circles will lie exactly on top of each other?
  1. Since a circle is defined as a set of points a certain distance from a center, all the points on circle B will now be the same distance away from A as the points on circle A.
  2. Because a dilation is a rigid transformation, all the points on circle B must move by the same amount.
  3. Since the centers of the two circles are coincident, the rest of the circle must also be coincident.
  4. We can't be sure and need to use more radii from each circle to show this.
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