MathDB
Weighted Fermat

Source: 2016 Korean Winter Camp 2nd Test #7

January 25, 2016
geometryalgebraconics

Problem Statement

Let there be a triangle △ABC\triangle ABC with BC=aBC=a, CA=bCA=b, AB=cAB=c. Let TT be a point not inside △ABC\triangle ABC and on the same side of AA with respect to BCBC, such that BT−CT=c−bBT-CT=c-b. Let n=BTn=BT and m=CTm=CT. Find the point PP that minimizes f(P)=−a⋅AP+m⋅BP+n⋅CPf(P)=-a \cdot AP + m \cdot BP + n \cdot CP.
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