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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 Problem Solving

In the above diagram, $d_1=24$ and $d_2=18.$ What is the perimeter of the green colored region?

{84}\pi

{78}\pi

{48}\pi

{42}\pi

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by Brilliant Staff

In the above image of a circle with center at $O,$ $\angle ABC = 115 ^ \circ$ . What is angle $AOC$ (as marked) equal to?

130 ^ \circ

65 ^ \circ

230 ^ \circ

115 ^ \circ

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by Brilliant Staff

The length of each side in the above square is $14.$ If the two curves in the square are each one quarter of a circle with radius $14,$ calculate the area of the region bounded by the two curves in the above diagram.

98\pi - 196

392\pi - 196

14\pi - 392

196\pi - 98

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by Brilliant Staff

$\Gamma$ is a circle with center $O$ . $A$ and $B$ are points on $\Gamma$ such that the sector $AOB$ has perimeter $80$ . What is the maximal possible area of sector $AOB$ ?

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by Brilliant Staff

Let $O_1$ and $O_2$ be the centers of two circles with the same radius $15\text{ cm}.$ What is the perimeter of the green colored region?

{15}\pi \text{ cm}

{5}\pi \text{ cm}

{20}\pi \text{ cm}

{30}\pi \text{ cm}

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by Brilliant Staff

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