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.
by
Gaurav Agarwal