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Triangle inside triangle

Source: Argentina IberoAmerican TST 2024 P3

August 9, 2024
geometryperpendicular bisector

Problem Statement

Let ABCABC be an acute scalene triangle and let MM be the midpoint of side BCBC. The angle bisector of the ∠BAC\angle BAC, the perpendicular bisector of the side ABAB and the perpendicular bisector of the side ACAC define a new triangle. Let HH be the point of intersection of the three altitudes of this new triangle. Show that HH belongs to line segment AMAM.
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