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BT+CT <= 2R - Iran NMO 2003 (Second Round) - Problem5

Source:

October 4, 2010
geometrycircumcircletrigonometryinequalitiestrapezoidgeometry proposed

Problem Statement

∠A\angle{A} is the least angle in ΔABC\Delta{ABC}. Point DD is on the arc BCBC from the circumcircle of ΔABC\Delta{ABC}. The perpendicular bisectors of the segments AB,ACAB,AC intersect the line ADAD at M,NM,N, respectively. Point TT is the meet point of BM,CNBM,CN. Suppose that RR is the radius of the circumcircle of ΔABC\Delta{ABC}. Prove that: BT+CT≤2R. BT+CT\leq{2R}.
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