The simplest right triangle with rational sides (the longest side has a denominator of 45 digits!) and area 157, was found by Don Zagier in 1993.

## A Paradoxical Zero-Length Hypotenuse

A strange right-triangle involving the unit imaginary number *i*

## A curious right triangle

The sides of a pentagon, hexagon, and decagon, inscribed in congruent circles, form a right triangle.

## Sangaku: Semicircle inscribed in a right triangle

Find the radius* r* of the semicircle inscribed in the right triangle below:

show solution