Come right inside, please

Calculus Level 2

Let $S$ be the maximum possible area of a right triangle that can be drawn in a semi-circle of radius $1$ , where one of the legs (and not the hypotenuse) of the triangle must lie on the diameter of the semicircle.

If $S = \dfrac{a\sqrt{b}}{c},$ where $a,c$ are positive coprime integers and $b$ is a positive square-free integer, find $a + b + c.$

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.