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Part of 1990 Baltic Way

Problems(1)

Equilateral triangle erected on a side defines another

Source:

4/19/2013
Let ABCDABCD be a quadrilateral with AD=BCAD = BC and ∠DAB+∠ABC=120∘\angle DAB + \angle ABC = 120^\circ. An equilateral triangle DPCDPC is erected in the exterior of the quadrilateral. Prove that the triangle APBAPB is also equilateral.
geometryperpendicular bisector