3

Part of 2007 Vietnam National Olympiad

Problems(2)

Vietnamese national Olympiad 2007, problem 3

Source:

Let B,C be fixed points and A be roving point. Let H, G be orthecentre and centroid of triagle ABC. Known midpoint of HG lies on BC, find locus of A

analytic geometrygeometryconicshyperbolageometry unsolved

Vietnamese national Olympiad 2007, problem 6

Source:

Let ABCD be trapezium that is inscribed in circle (O) with larger edge BC. P is a point lying outer segment BC. PA cut (O) at N(that means PA isn't tangent of (O)), the circle with diameter PD intersect (O) at E, DE meet BC at N. Prove that MN always pass through a fixed point.

geometrytrapezoidgeometry unsolved