P is a point inside ABC. BP, CP intersect AC,AB at E,F, respectively. AP intersect ⊙(ABC) again at X. ⊙(ABC) and ⊙(AEF) intersect again at S. T is a point on BC such that PT∥EF. Prove that ⊙(STX) passes through the midpoint of BC.proposed by chengbilly geometrymidpointConcyclic