Hello, realintegerz!

A triangle is incribed in a semicircle of radius 1,

two of the vertices are *on the ends of the diameter*

and the third vertex is somewhere on the semicircle.

Find a rule that describes the area of the triangle as a function

of the length of the shortest side of the triangle. Code:

* * * C
* *
. . . * * \*
. . . * * a\*
. . . * \*
. . A * - - - - + - - - - * B
. . . 1 O 1

is inscribed in a semicircle

. . with center and radius

Let the shortest side be

Since is a right triangle: .

. .

The area of the triangle is: .

Therefore: .