Triangles into each other
Source: Iran TST 2015 Test 3 Day 2 P1
August 18, 2023
geometry
Problem Statement
Ali puts points on the plane such that no three of them are collinear. Ramtin adds a sixth point that is not collinear with any two of the former points.Ali wants to eventually construct two triangles from the six points such that one can be placed inside another. Can Ali put the 5 points in such a manner so that he would
always be able to construct the desired triangles? (We say that triangle can be
placed inside triangle if is congruent to a triangle that is located completely
inside .)