MathDB

1

Part of 2005 Cono Sur Olympiad

Problems(2)

Cono Sur Olympiad 2005, Problem 1

Source:

8/19/2014
Let ana_n be the last digit of the sum of the digits of 20052005...200520052005...2005, where the 20052005 block occurs nn times. Find a1+a2+⋯+a2005a_1 +a_2 + \dots +a_{2005}.
number theory proposednumber theory
Cono Sur Olympiad 2005, Problem 4

Source:

8/19/2014
Let ABCABC be a isosceles triangle, with AB=ACAB=AC. A line rr that pass through the incenter II of ABCABC touches the sides ABAB and ACAC at the points DD and EE, respectively. Let FF and GG be points on BCBC such that BF=CEBF=CE and CG=BDCG=BD. Show that the angle ∠FIG\angle FIG is constant when we vary the line rr.
geometryincentergeometric transformationreflectionsymmetryperpendicular bisectorgeometry proposed