MathDB

new triangle has area 1/7 of original equilateral

Source: Eotvos 1942 p3

September 10, 2024

geometryareasEquilateral

Problem Statement

Let

A'

,

B'

and

C'

be points on the sides

BC

,

BA' = 2A'C

and

AB

, respectively, of an equilateral triangle

ABC

. If

AC' = 2C'B

,

BA' = 2A'C

and

CB' = 2B'A

, prove that the lines

AA'

,

BB'

and

CC'

enclose a triangle whose area is

1/7

that of

ABC

.

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