MathDB

6

Part of 2016 Postal Coaching

Problems(2)

Subset of 63 points

Source: India Postal Set 2 P6 2016

1/18/2017
Consider a set of 20162016 distinct points in the plane, no four of which are collinear. Prove that there is a subset of 6363 points among them such that no three of these 6363 points are collinear.
combinatoricscombinatorial geometry
Three lines meet - or actually, they don't

Source: India Postal Set 6 P6 2016

1/18/2017
Let KK and LL be the centers of the excircles of a non-isosceles triangle ABCABC opposite BB and CC respectively. Let MM and NN be points in the plane of the triangle such that BMBM bisects ACAC and CNCN bisects ABAB. Prove that the lines KMKM and NKNK meet on BCBC.
The problem in its current formulation is trivially wrong. No possible rectification is known to OP / was sent to the participants.
geometry