MathDB
PB = PA + PC, equilateral , iff form (2009 Indonedia MO Province P2 q4 OSP)

Source:

December 11, 2020
geometrycircumcircleEquilateral

Problem Statement

Given an equilateral triangle ABCABC and a point PP so that the distances PP to AA and to CC are not farther than the distances PP to BB. Prove that PB=PA+PCPB = PA + PC if and only if PP lies on the circumcircle of △ABC\vartriangle ABC.
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