Question 64
In an isosceles triangle $ABC$ with $AB = BC$, points $K$ and $M$ are the midpoints of the sides $AB$ and $AC$, respectively. The circumscribed circle of the triangle $CKB$ meets the line $BM$ at point $N$ different from $B$. The line passing through $N$ parallel to the side $AC$ meets the circumscribed circle of the triangle $ABC$ at points $A_1$ and $C_1$.
Prove that the triangle $A_1BC_1$ is equilateral.
Prove that the triangle $A_1BC_1$ is equilateral.