Let ABC be an acute triangle with ∠BAC=30∘. The internal and external angle bisectors of ∠ABC meet the line AC at B1 and B2, respectively, and the internal and external angle bisectors of ∠ACB meet the line AB at C1 and C2, respectively. Suppose that the circles with diameters B1B2 and C1C2 meet inside the triangle ABC at point P. Prove that ∠BPC=90∘ . geometrygeometric transformationreflectioncircumcirclecomplex numbersgeometry proposed