MathDB

5

Part of 2007 Postal Coaching

Problems(2)

N points, total number of pairwise distances of these N points is at most n

Source: Indian Postal Coaching 2007 set 3 p5

5/25/2020
There are NN points in the plane such that the total number of pairwise distances of these NN points is at most nn. Prove that N≤(n+1)2N \le (n + 1)^2.
combinatoricscombinatorial geometrydistance
concurrent Euler lines

Source: Indian Postal Coaching 2007 set 6 p5

5/25/2020
Let PP be an interior point of triangle ABCABC such that ∠BPC=∠CPA=∠APB=120o\angle BPC = \angle CPA =\angle APB = 120^o. Prove that the Euler lines of triangles APB,BPC,CPAAPB,BPC,CPA are concurrent.
Euler Lineconcurrentgeometryequal angles