Yeah Geometry Rocks

Geometry Level 3

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

Construct a triangle ABC with side lengths BC=a,CA=b,AB=cBC = a, CA = b, AB = c.

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

Find DA+DB+DCDA+DB+DC.

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