1/3 is a nice number for this case

Discrete Mathematics Level 3

Circles $L$ and $l$ share the same center. Circle $L$ has radius $3r$ and circle $l$ has radius $r.$ Points $A, B, C$ are chosen on the circumference of circle $L$ uniformly at random.

What is the probability that the centroid of $\triangle ABC$ lies in the interior of circle $l$ ?

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 7 million people

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