Two vertices A,B of a triangle ABC are located on a parabola y=ax² + bx + c with a>0 in such a way that the sides AC,BC are tangent to the parabola. Let m_c be the length of the median CC₁ of triangle ABC and S be the area of triangle ABC. Find S²/m_c³

I graphed it all in Desmos, but I haven't worked out the algebra.  It looks like lots of things eventually cancel out.

Posted by Jer on 2023-08-25 16:18:28