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Geometry

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, interactive explorations.

Used and loved by over 5 million people

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

Your answer seems reasonable. Find out if you're right!

That seems reasonable. Find out if you're right!

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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?

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

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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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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, interactive explorations.

Used and loved by over 5 million people

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

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, interactive explorations.

Used and loved by over 5 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

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

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