MathDB

1

Part of 2007 Turkey Team Selection Test

Problems(2)

graph

Source: turkey TST 2007

4/10/2007
Find the number of the connected graphs with 6 vertices. (Vertices are considered to be different)
combinatorics proposedcombinatorics
Two triangles

Source: Turkey TST 2007

4/10/2007
Let ABCABC is an acute angled triangle and let A1, B1, C1A_{1},\, B_{1},\, C_{1} are points respectively on BC, CA, ABBC,\,CA,\,AB such that △ABC\triangle ABC is similar to △A1B1C1.\triangle A_{1}B_{1}C_{1}. Prove that orthocenter of A1B1C1A_{1}B_{1}C_{1} coincides with circumcenter of ABCABC.
geometrycircumcircleanalytic geometrytrigonometrygeometry proposed