Let O be the center of the equilateral triangle ABC. Pick two points P1 and P2 other than B, O, C on the circle ⊙(BOC) so that on this circle B, P1, P2, O, C are placed in this order. Extensions of BP1 and CP1 intersects respectively with side CA and AB at points R and S. Line AP1 and RS intersects at point Q1. Analogously point Q2 is defined. Let ⊙(OP1Q1) and ⊙(OP2Q2) meet again at point U other than O.Prove that 2∠Q2UQ1+∠Q2OQ1=360∘.Remark. ⊙(XYZ) denotes the circumcircle of triangle XYZ. geometry proposedgeometry