## 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, conceptual quizzes.

## Our wiki is made for math and science

###
Master advanced concepts through explanations,

examples, and problems from the community.

## Used and loved by 4 million people

###
Learn from a vibrant community of students and enthusiasts,

including olympiad champions, researchers, and professionals.

## Comments

Sort by:

TopNewestLet the length of one leg be \(\sqrt{2}\). Then we can calculate the semiperimeter as \(1+\sqrt{2}\), and thus the radius of the inscribed circle as \(\frac{1}{1+\sqrt{2}}\). The area is then \(\pi(\sqrt{2}-1)\). The next two figures are quite simple, we see that in the upper-right figure, the square is half of the area of the triangle, and in the last figure, the side length of the square is \(\frac{1}{3}\) of the hypotenuse, thus the area is \(4/9\). Computing, we find that the circle contains the largest area. – Finn Hulse · 2 years, 3 months ago

Log in to reply