In any acute triangle, the inscribed triangle with the smallest perimeter is the orthic triangle. This is the solution to Fagnano's problem, posed in 1775. The sides of the orthic triangle are parallel to the tangents to the circumcircle at the original triangle's vertices.
in any acute triangle the inscribed triangle with the smallest perimeter is the orthic triangle this is the solution to fagnano's problem posed in 1775 the sides of the orthic triangle are parallel to the tangents to the circumcircle at the original triangle's vertices