MathDB
almost easy [prove < ROS = < BAC]

Source: iran2004 (geo exam)

September 10, 2004
geometrycircumcirclegeometric transformationprojective geometrytrigonometryanalytic geometrycalculus

Problem Statement

Let ABCABC be a triangle, and OO the center of its circumcircle. Let a line through the point OO intersect the lines ABAB and ACAC at the points MM and NN, respectively. Denote by SS and RR the midpoints of the segments BNBN and CMCM, respectively. Prove that ∡ROS=∡BAC\measuredangle ROS=\measuredangle BAC.
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