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MA.912.G.6.5 Measures of Circles

What You Need To Know...

Circumference, arc length, and areas of circles and sectors.

  1. The benchmark will be assessed using MC (Multiple Choice) and FR (Fill in Response) items.
  2. All angle measurements will be in degrees.
  3. Formal or informal proofs completions may be required.
  4. Items may include references to circumference, radius, diameter, arc, arc length, chord, secant, tangent and concentric circles.
  5. Items may include central angles, inscribed angles and intersections of secants and tangents.

Example One

Allison created an embroidery design of a stylized star emblem.  The perimeter of the design is made by alternating semicircle and quarter-circle arcs.  Each arc is formed from a circle with a 2½-inch diameter.  There are 4 semicircle and 4 quarter-circle arcs, as shown in the diagram below.


To the nearest whole inch, what is the perimeter of Allison's design?

  1. 15 inches
  2. 20 inches
  3. 24 inches
  4. 31 inches


Example Two

Kayla inscribed kite ABCD in a circle, as shown below.


If the measure of arc ADC is 255° in Kayla's design, what is the measure, in degrees, of  ∠ ADC?

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Additional Examples


Circle Basics
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Area of a Circle
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Concentric Circles
Arc Measure & Arc Length
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Chord Properties
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Central & Inscribed Angles
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Secants and Tangents
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Reference Sheet