MathDB

In a plane, the six different points

A, B, C, A', B', C'

are given such that triangles

ABC

and

A'B'C'

are congruent, i.e.

AB=A'B', BC=B'C', CA=C'A'.

Let

G

be the centroid of

ABC

and

A_1

be an intersection point of the circle with diameter

AA'

and the circle with center

A'

and passing through

G.

Define

B_1

and

C_1

similarly. Prove that

AA_1^2+BB_1^2+CC_1^2 \leq AB^2+BC^2+CA^2

Problem Statement