MathDB

2

Part of 1994 Vietnam National Olympiad

Problems(2)

condition on $ABC$ for $A'B'C'$ to be equilateral.

Source: 32-th Vietnamese Mathematical Olympiad 1994

2/24/2007
ABCABC is a triangle. Reflect each vertex in the opposite side to get the triangle A′B′C′A'B'C'. Find a necessary and sufficient condition on ABCABC for A′B′C′A'B'C' to be equilateral.
geometrygeometric transformationreflectiontrigonometrycircumcirclegeometry proposed
sphere

Source: 32-th Vietnamese Mathematical Olympiad 1994

2/24/2007
SS is a sphere center O.GO. G and G′G' are two perpendicular great circles on SS. Take A,B,CA, B, C on GG and DD on G′G' such that the altitudes of the tetrahedron ABCDABCD intersect at a point. Find the locus of the intersection.
geometry3D geometryspheretetrahedronvectoranalytic geometrygeometry unsolved