MathDB

3

Part of 2016 Bundeswettbewerb Mathematik

Problems(2)

Perpendicular lines due to circle

Source: Germany 2016 - BWM Round 1, #3

11/12/2016
Let A,B,CA,B,C and DD be points on a circle in this order. The chords ACAC and BDBD intersect in point PP. The perpendicular to ACAC through C and the perpendicular to BDBD through DD intersect in point QQ. Prove that the lines ABAB and PQPQ are perpendicular.
geometrygeometry unsolvedperpendicularcirclechordGermany
Just like an old Putnam FE...

Source: Bundeswettbewerb Mathematik 2016, Round 2 - #3

9/7/2016
Find all functions ff that is defined on all reals but 13\tfrac13 and −13- \tfrac13 and satisfies f(x+11−3x)+f(x)=x f \left(\frac{x+1}{1-3x} \right) + f(x) = x for all x∈R∖{±13}x \in \mathbb{R} \setminus \{ \pm \tfrac13 \}.
functionPutnamalgebrafunctional equation