MathDB

2

Part of 1998 Turkey MO (2nd round)

Problems(2)

An Easy Inequality on three variables

Source: Turkish NMO 1998, 2. Problem

7/31/2011
If 0≤a≤b≤c0\le a\le b\le c real numbers, prove that (a+3b)(b+4c)(c+2a)≥60abc(a+3b)(b+4c)(c+2a)\ge 60abc.
inequalitiessearchinequalities proposed
Geometric locus problem about a constant sum

Source: Turkish NMO 1998, 5. Problem

7/31/2011
Variable points MM and NN are considered on the arms [OX\left[ OX \right. and [OY\left[ OY \right. , respectively, of an angle XOYXOY so that ∣OM∣+∣ON∣\left| OM \right|+\left| ON \right| is constant. Determine the locus of the midpoint of [MN]\left[ MN \right].
geometrygeometric transformationreflectionparallelogramangle bisectorgeometry proposedHjelmslev