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Geometry

Properties of Circles

Concept Quizzes

Properties of Circles Warmup
Circles - Radius and Diameter and Circumference
Circles - Area
Circles - Central Angles
Circles - Inscribed Angles
Circles - Arc Length
Circles - Sector Area
Circles Problem Solving

Challenge Quizzes

Circle Properties: Level 1 Challenges
Circle Properties: Level 2 Challenges
Circle Properties: Level 3 Challenges

Circles - Central Angles

In the above diagram, if the radius of the circle is $18$ and the angle $AOB$ (central angle) is ${30}^\circ,$ what is the measure of the arc $\widehat{AB} ?$

6\pi

3\pi

9\pi

1\pi

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by Brilliant Staff

In the above diagram, if angle $COD$ is $\theta_2={123}^\circ$ and the measures of arc $\widehat{AB}$ and arc $\widehat{CD}$ are $5\text{ cm}$ and $15\text{ cm},$ respectively, what is the angle $\theta_1 (= \angle AOB)?$

50^\circ

53^\circ

35^\circ

41^\circ

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by Brilliant Staff

In the above diagram, $\overline{AB}$ is a diameter of the circle centered at $O$ , $\overline{AB} \parallel \overline{DC}$ , and $\angle BOC=\theta={30}^\circ.$ If the measure of the arc $\widehat{BC}$ is $l_1=12\pi\text{ cm},$ what is the measure of the arc $\widehat{CD} ?$

48 \text{ cm}

58\pi \text{ cm}

48\pi \text{ cm}

58 \text{ cm}

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by Brilliant Staff

In the above diagram, $\overline{AB}$ is a diameter of the circle centered at $O,$ and $\lvert{\overline{OD}}\rvert=\lvert{\overline{DE}}\rvert$ and $\angle E=\theta={15}^\circ.$ If the measure of the arc $\widehat{BD}$ is $5\text{ cm},$ what is the measure of the arc $\widehat{AC}$ in $\text{cm} ?$

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by Brilliant Staff

Imagine a circle divided into equal sectors via $n$ straight lines that cross point $O$ , the center of the circle. Let sector $ABO$ be one of those sectors. When $n=20,$ what is $\angle OAB$ in degrees? (Round down to the nearest degree if there is a decimal.)

80 95 90 85

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by Brilliant Staff