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"(45) \\DeltaABC is equilateral. Point in on \\( \\overline { B C } \\) is sulh that \\( B P = \\frac { 1 } { 4 } 8 C \\)\nProve that \\( 13 A B ^ { 2 } = 16 A P ^ { 2 } \\)."

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