Re: [math-fun] Hopefully trivial question about triangles

If you inscribe a triangle within another triangle, so that the inscribed triangle vertices actually touch the 3 sides of the larger triangle, what is the shape of the inscribed triangle of _minimum perimeter_ ? Is it the tangent points of the inscribed circle?

for acute triangles, it is the "pedal triangle", obtained by joining the feet of the altitudes of the triangle. for right and obtuse triangles, the answer degenerates to the "triangle" which has two vertices at the right/obtuse angle, and whose other vertex is the foot of the altitude from the right/obtuse angle. mike