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perpenidicularity, joining arc midpoints

Source: Polish MO Second Round 1964 p2

August 31, 2024
geometryperpendiculararc midpoint

Problem Statement

The circle is divided into four non-overlapping gaps AB AB , BC BC , CD CD and DA DA . Prove that the segment joining the midpoints of the arcs ABAB and CDCD is perpendicular to the segment joining the midpoints of the arcs BCBC and DADA.
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