MathDB
TOT 288 1991 Spring A J4 perpendicular, rotate an arc

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June 9, 2024
rotationgeometryperpendicular

Problem Statement

A circle is divided by the chord ABAB into two segments and one of them is rotated about the point AA by a certain angle, the point BB being taken to BB'. Prove that the line segments joining the midpoints of the two arcs (i.e. the arc ABAB which had not been rotated and the rotated arc ABAB') with the midpoint of BBBB' are perpendicular.
(F. Nazyrov, 11th form student, Obninsk)