MathDB

sum is over the consecutive square of the segments

Source: China TST 1986, problem 4

May 16, 2005

inductiongeometrygeometry unsolved

Problem Statement

Given a triangle

ABC

for which

C=90

degrees, prove that given

n

points inside it, we can name them

P_1, P_2 , \ldots , P_n

in some way such that:

\sum^{n-1}_{k=1} \left( P_K P_{k+1} \right)^2 \leq AB^2

(the sum is over the consecutive square of the segments from

1

up to

n-1

). Edited by orl.