ω is circumcirlce of triangle ABC. We draw a line parallel to BC that intersects AB,AC at E,F and intersects ω at U,V. Assume that M is midpoint of BC. Let ω′ be circumcircle of UMV. We know that R(ABC)=R(UMV). ME and ω′ intersect at T, and FT intersects ω′ at S. Prove that EF is tangent to circumcircle of MCS. geometrycircumcirclepower of a pointradical axisperpendicular bisectorgeometry proposed