MathDB

There were ten points

X_1, \ldots , X_{10}

on a line in this particular order. Pete constructed an isosceles triangle on each segment

X_1X_2, X_2X_3,\ldots, X_9X_{10}

as a base with the angle

\alpha{}

at its apex. It so happened that all the apexes of those triangles lie on a common semicircle with diameter

X_1X_{10}

. Find

\alpha{}

.
Egor Bakaev

Problem Statement