MathDB

6

Part of 2018 Caucasus Mathematical Olympiad

Problems(2)

Easy geometric inequality

Source: III Caucasus Mathematical Olympiad

3/17/2018
Given a convex quadrilateral ABCDABCD with ∠BCD=90∘\angle BCD=90^\circ. Let EE be the midpoint of ABAB. Prove that 2EC⩽AD+BD2EC \leqslant AD+BD.
geometrygeometric inequalityinequalities
Fuss lemma for parabolas

Source: III Caucasus Mathematical Olympiad

3/17/2018
Two graphs G1G_1 and G2G_2 of quadratic polynomials intersect at points AA and BB. Let OO be the vertex of G1G_1. Lines OAOA and OBOB intersect G2G_2 again at points CC and DD. Prove that CDCD is parallel to the xx-axis.
algebraquadratic trinomialconicsparabola