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fixed midpoint of bases of isosceles triangles coincide, fixed angle

Source: Tournament of Towns, Junior O-Level , Spring 2019 p4

May 9, 2020
fixedFixed pointisoscelesgeometry

Problem Statement

Isosceles triangles with a fixed angle α\alpha at the vertex opposite to the base are being inscribed into a rectangle ABCDABCD so that this vertex lies on the side BCBC and the vertices of the base lie on the sides ABAB and CDCD. Prove that the midpoints of the bases of all such triangles coincide.
(Igor Zhizhilkin)
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