Circulisious

Geometry Level 2

Given a sector of radius 10 and angle $\frac{ \pi}{3}$ , we draw the largest circle (in green) that is tangent to all sides of the sector. We then draw the circle (in pink) that is tangent to the 2 sides, and also to the green circle. We repeat this process indefinately, where the next circle is shown in blue.

Find the sum of the areas of these infinitely many 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 8 million people

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