MathDB

2

Part of 1980 Bundeswettbewerb Mathematik

Problems(2)

Bundeswettbewerb Mathematik 1980 Problem 1.2

Source: Bundeswettbewerb Mathematik 1980 Round 1

9/23/2022
In a triangle ABCABC, the bisectors of angles AA and BB meet the opposite sides of the triangle at points DD and EE, respectively. A point PP is arbitrarily chosen on the line DEDE. Prove that the distance of PP from line ABAB equals the sum or the difference of the distances of PP from lines ACAC and BCBC.
geometrybisectorsdistanceTriangle
NT PHP in subset of N

Source: Yugoslav TST 1990 P3

5/28/2021
Prove that from every set of n+1n+1 natural numbers, whose prime factors are in a given set of nn prime numbers, one can select several distinct numbers whose product is a perfect square.
number theorycombinatoricslinear algebra