Find the smallest obtuse triangle such that its sides, the altitude to the obtuse angle, and the median to the largest side are all integers.

In case it arises, "smallest" refers to the area of the triangle.

The official solution palms off the 5,5,6 triangle as obtuse, but it isn't.  The big angle is twice the small angle of a 3,4,5 right triangle.  This was already pointed out by Dej Mar in a comment  that appeared long before the official solution was posted.

Posted by Richard on 2006-05-19 13:40:44