Let be a point inside such that

MATHEMATICS · Subjective · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

Let PP be a point inside △ABC\triangle ABC such that ∠APB=∠BPC=∠CPA\angle APB=\angle BPC=\angle CPA. Prove that PA+PB+PC=a2+b2+c22+23Δ,PA+PB+PC=\sqrt{\frac{a^2+b^2+c^2}{2}+2\sqrt{3}\Delta}, where aa, bb, cc are the side lengths and Δ\Delta is the area of △ABC\triangle ABC.

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