Yeah Geometry Rocks

Geometry Level 3

A point inside an equilateral triangle with side 1 is at distance \(a, b, c\) from the vertices.

Construct a triangle ABC with side lengths \(BC = a, CA = b, AB = c\).

Let D be a point in ABC such that \( \angle ADB = \angle BDC = \angle CDA =120^\circ\).

Find \(DA+DB+DC\).

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