MathDB

An equilateral triangle of altitude

1

is considered. For every point

P

on the interior of the triangle, denote by

x, y , z

the distances from the point

P

to the sides of the triangle. a) Prove that for every point

P

inside the triangle it is true that

x + y + z = 1

. b) For which points of the triangle does it hold that the distance to one side is greater than the sum of the distances to the other two? c) We have a bar of length

1

and we break it into three pieces. find the probability that with these pieces a triangle can be formed.

Problem Statement