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Betal marks

2021

points on the plane such that no three are collinear, and draws all possible segments joining these. He then chooses any

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of these segments, and marks their midpoints. Finally, he chooses a segment whose midpoint is not marked yet, and challenges Vikram to construct its midpoint using only a straightedge. Can Vikram always complete this challenge?
Note. A straightedge is an infinitely long ruler without markings, which can only be used to draw the line joining any two given distinct points.
Proposed by Prithwijit De and Sutanay Bhattacharya

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Problems(1)