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2020 IGO Intermediate P2

Source: 7th Iranian Geometry Olympiad (Intermediate) P2

November 4, 2020
rectanglecircumcircleanglesTrianglegeometryIGO

Problem Statement

Let ABCABC be an isosceles triangle (AB=ACAB = AC) with its circumcenter OO. Point NN is the midpoint of the segment BCBC and point MM is the reflection of the point NN with respect to the side ACAC. Suppose that TT is a point so that ANBTANBT is a rectangle. Prove that ∠OMT=12∠BAC\angle OMT = \frac{1}{2} \angle BAC.
Proposed by Ali Zamani
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