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possible areas for a triangle, arc midpoint, orthocenter and a vertex collinear

Source: Canada Repêchage 2024/3 CMOQR

March 25, 2024
geometryareasarc midpoint

Problem Statement

Let △ABC\vartriangle ABC be an acute triangle with AB<ACAB < AC. Let HH be its orthocentre and MM be the midpoint of arc BACBAC on the circumcircle. It is given that BB, HH, MM are collinear, the length of the altitude from MM to ABAB is 11, and the length of the altitude from MM to BCBC is 66. Determine all possible areas for △ABC\vartriangle ABC .
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