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Turkish NMO 1998, 1. Problem, points in a isosceles triangle

Source:

July 31, 2011
geometry proposedgeometry

Problem Statement

Let DD be the point on the base BCBC of an isosceles △ABC\vartriangle ABC triangle such that ∣BD∣∣DC∣= 2\frac{\left| BD \right|}{\left| DC \right|}=\text{ }2, and let PP be the point on the segment [AD]\left[ AD \right] such that ∠BAC=∠BPD\angle BAC=\angle BPD. Prove that ∠DPC=12∠BAC\angle DPC=\frac{1}{2}\angle BAC.
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