Let ABC be a triangle, and O the center of its circumcircle.
Let a line through the point O intersect the lines AB and AC at the points M and N, respectively. Denote by S and R the midpoints of the segments BN and CM, respectively.
Prove that ∡ROS=∡BAC. geometrycircumcirclegeometric transformationprojective geometrytrigonometryanalytic geometrycalculus