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concurrency defined by angles and lines of unit circle

Source: Sharygin 2006 VIII-X CR 9

August 23, 2019
anglesgeometrycircleconcurrentconcurrency

Problem Statement

L(a)L(a) is the line connecting the points of the unit circle corresponding to the angles aa and π−2a\pi - 2a. Prove that if a+b+c=2πa + b + c = 2\pi, then the lines L(a),L(b)L (a), L (b) and L(c)L (c) intersect at one point.
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