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Tags: geometry, inequalities, circumcircle, trigonometry, geometry unsolved



Let $P$ be a point inside a triangle $ABC$ such that \[\angle P AB = \angle P BC = \angle P CA\] Suppose $AP, BP, CP$ meet the circumcircles of triangles $P BC, P CA, P AB$ at $X, Y, Z$ respectively $(\neq P)$ . Prove that \[[XBC] + [Y CA] + [ZAB] \ge 3[ABC]\]