MathDB

4

Part of 2008 IberoAmerican Olympiad For University Students

Problems(1)

AC,BC tangent to parabola - OIMU 2008 Problem 4

Source:

8/28/2010
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}
conicsparabolageometrygeometry proposed