MathDB

1

Part of 2012 Czech-Polish-Slovak Junior Match

Problems(2)

concurrency starting with the symmetric points of an interior wrt midpoints

Source: Czech-Polish-Slovak Junior Match 2012, Individual p1 CPSJ

3/11/2020
Point PP lies inside the triangle ABCABC. Points K,L,MK, L, M are symmetrics of point PP wrt the midpoints of the sides BC,CA,ABBC, CA, AB. Prove that the straight AK,BL,CMAK, BL, CM intersect at one point.
concurrencyconcurrentsymmetrymidpointsgeometry
max no of real numbers in a board such for any 2 their product is included

Source: Czech-Polish-Slovak Junior Match 2012, Team p1 CPSJ

3/12/2020
There are a lot of different real numbers written on the board. It turned out that for each two numbers written, their product was also written. What is the largest possible number of numbers written on the board?
maxcombinatoricsProduct