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angles of orthic triangles,

Source: 1965 Swedish Mathematical Competition p1

March 21, 2021
Geometric Inequalitiesaltitudesgeometryanglesmax

Problem Statement

The feet of the altitudes in the triangle ABCABC are A′,B′,C′A', B', C'. Find the angles of A′B′C′A'B'C' in terms of the angles A,B,CA, B, C. Show that the largest angle in A′B′C′A'B'C' is at least as big as the largest angle in ABCABC. When is it equal?
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