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AC,BC tangent to parabola - OIMU 2008 Problem 4

Source:

August 28, 2010
conicsparabolageometrygeometry proposed

Problem Statement

Two vertices A,BA,B of a triangle ABCABC are located on a parabola y=ax2+bx+cy=ax^2 + bx + c with a>0a>0 in such a way that the sides AC,BCAC,BC are tangent to the parabola. Let mcm_c be the length of the median CC1CC_1 of triangle ABCABC and SS be the area of triangle ABCABC. Find S2mc3\frac{S^2}{m_c^3}
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