From the Codechef Contest (problem and [solution] https://discuss.codechef.com/t/pizza-slice-xypizq-mini-editorial/21639 , https://discuss.codechef.com/t/xypizq-editorial/21634 ):
ChefX showed ChefY his new pizza slice design. The design is a planar figure that can be drawn in the following way:
Draw a point $A0$ and two rays from this point such that the angle between them is $α<π/2.$
Mark N points $A1,A2,A3,…,AN$ on one ray in this order ($A1$ is closest to $A0$).
Mark N points $B1,B2,B3,…,BN$ on the other ray in this order ($B1$ is closest to $A0$).
For each valid i, draw a line segment between points Ai and Bi+1.
For each valid i, draw a line segment between points Bi and Ai+1.
Finally, draw a line segment between points AN and BN.
All these 2N−1 line segments must have equal lengths, which must also be equal to $|A0A1|=|A0B1|.$
Can you help ChefX find the angle ChefY asks for? It can be proved that under the given constraints, each angle can be written as π⋅m/n, where m and n are coprime integers; you should find m and n.
In short, I am not able to understand the author's solution for calculating any angle in the triangle. Also, the author's solution says that the pizza slice is always an isosceles triangle...how can that be proved ?