MathDB
Normal Geometry Problem

Source: 2017 Taiwan TST Round 3

April 13, 2018
geometrycircumcircle

Problem Statement

△ABC\triangle ABC satisfies ∠A=60∘\angle A=60^{\circ}. Call its circumcenter and orthocenter O,HO, H, respectively. Let MM be a point on the segment BHBH, then choose a point NN on the line CHCH such that HH lies between C,NC, N, and BM‾=CN‾\overline{BM}=\overline{CN}. Find all possible value of MH‾+NH‾OH‾\frac{\overline{MH}+\overline{NH}}{\overline{OH}}
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