How can be described in other words the class of triangles, in which each altitude is less than each side?
I tried to solve the problem analytically, using the formulas for the altitudes as functions of the sides, but the result was a system of six algebraic inequalities of degree 4. I couldn't solve this system. Maybe there is a pure geometric approach?
I tried to solve the problem analytically, using the formulas for the altitudes as functions of the sides, but the result was a system of six algebraic inequalities of degree 4. I couldn't solve this system. Maybe there is a pure geometric approach?