MathDB

3

Part of 2006 Bundeswettbewerb Mathematik

Problems(2)

A²+b² > 5c²

Source: Germany Bundeswettbewerb Mathematik 2006, Day 1, Problem 3

4/4/2006
Let a,b,ca,b,c be the sidelengths of a triangle such that a2+b2>5c2a^2+b^2 > 5c^2 holds. Prove that cc is the shortest side of the triangle.
locus of point with equal angles

Source:

3/7/2007
A point PP is given inside an acute-angled triangle ABCABC. Let A′,B′,C′A',B',C' be the orthogonal projections of PP on sides BC,CA,ABBC, CA, AB respectively. Determine the locus of points PP for which ∠BAC=∠B′A′C′\angle BAC = \angle B'A'C' and ∠CBA=∠C′B′A′\angle CBA = \angle C'B'A'
geometrycircumcirclegeometry unsolved