Semi-semicircle

Geometry Level 4

Take a semicircle of radius \(R\) and one semicircle \(k\) times bigger and make them tangent like in the picture above. Then construct a \({{90}^{\circ }}\) arc through the midpoints of these 2 semicircles. If the shaded area is \(A\), calculate the ratio \(\dfrac{A}{kR^2}\).

Hint: Notice that all three centers are collinear.

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 6 million people

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