Problem Geometry 1586: Twice the Insight: Unveiling a Unique Area Relationship in Equilateral Triangles

A Fresh Perspective or a Forgotten Gem?

Is This Elegant Property of Equilateral Triangles a New Discovery, or Has It Been Known for Centuries?

Problem 1586 Statement

Consider the equilateral triangles ABC, CDE, and ADF. G is the midpoint of AB, and H is the midpoint of DE. Prove that the area of triangle ADF is twice that of quadrilateral AGDH.

Uncover and share solutions to this problem.

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