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The points $A_0, A_1, A_2, A_3, A_4$ divide a unit circle (circle of radius $1$)

Source: Eotvos 1899 p1

March 14, 2020
algebrageometry

Problem Statement

The points A0,A1,A2,A3,A4A_0, A_1, A_2, A_3, A_4 divide a unit circle (circle of radius 11) into five equal parts. Prove that the chords A0,A1,A0,A2A_0, A_1, A_0, A_2 satisfy (A0A1⋅A0A2)2=5(A_0A_1 \cdot A_0A_2)^2= 5
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