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Properties of Circles

What is pi? If the area of a circle is 49π, what is its circumference? If a circle is inscribed in a square, what is the ratio of the areas of the circle and the square?

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

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Our wiki is made for math and science

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Concept Quizzes

Properties of Circles Warmup
Radius and Diameter
Area of a Circle
Central Angle
Inscribed Angle
Arc Length
Area of Sector
Problem Solving

Challenge Quizzes

Level 1
Level 2
Level 3

Circle Properties: Level 1 Challenges

In the above figure, which shaded area is larger?

The small circles all have the same size.

Equal area Blue region Yellow region

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by Chung Kevin

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Which of these shapes has an area that is different from the rest?

C B A D None of them

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by Chung Kevin

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When sketching out Leonardo Da Turtle, I started out with a green circle of radius 2, and then added a blue band across his eyes. The circular arcs of the blue band each subtend an angle of 60 degress at the center. And 2 triangles to fill in the gap. Finally, I added eyes of diameter 1.

What is the (visible) area of the blue band?

\[ \frac{5}{3} \pi + 2 \sqrt{3} \] \[ \frac{5}{6} \pi + 2 \sqrt{3} \] \[ \frac{5}{6} \pi + 4 \sqrt{3} \] \[ \frac{5}{3} \pi + 4 \sqrt{3} \]

Excel in math and science

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by Chung Kevin

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Consider a triangle \(ABC\) with right angle \(A\), \(BC=5\) and \(AC=4.\) Three semicircles are drawn as in the figure above. Find the sum of the areas of the orange shaded regions.

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by Bogdan Rusu

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What is the perimeter of a semicircle with radius 7?

Use the approximation \( \pi \approx 22/7 \).

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by ahmed gamaleddin

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Waste less time on Facebook — follow Brilliant.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Courses

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Community

100 Day Summer Challenge

Properties of Circles

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Concept Quizzes

Challenge Quizzes

Circle Properties: Level 1 Challenges

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.