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minimize 5 PA + 4 PB + 3 PC, for P interior point of triangle

Source: Vietnam MO 1978 P3

July 29, 2018
geometryminimumTriangle

Problem Statement

The triangle ABCABC has angle A=30oA = 30^o and AB=34ACAB = \frac{3}{4} AC. Find the point PP inside the triangle which minimizes 5PA+4PB+3PC5 PA + 4 PB + 3 PC.
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