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OM + ON >= R

Source: IV Soros Olympiad 1997-98 R3 9.3 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

June 1, 2024
geometrygeometric inequality

Problem Statement

Through point OO - the center of a circle circumscribed around an acute triangle - a straight line is drawn, perpendicular to one of its sides and intersecting the other two sides of the triangle (or their extensions) at points MM and NN. Prove that OM+ON≥ROM+ON \ge R, where RR is the radius of the circumscribed circle around the triangle.
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