Question 119
Three circular arcs $w_{1}$, $w_{2}$, $w_{3}$ with common endpoints $A$ and $B$ are on the same side of the line $AB$; $w_{2}$ lies between $w_{1}$ and $w_{3}$. Two rays emanating from $B$ intersect these arcs at $M_{1}$, $M_{2}$, $M_{3}$ and $K_{1}$, $K_{2}$, $K_{3}$, respectively. Prove that
$$
\frac{M_{1} M_{2}}{M_{2} M_{3}} = \frac{K_{1} K_{2}}{K_{2} K_{3}}.
$$
$$
\frac{M_{1} M_{2}}{M_{2} M_{3}} = \frac{K_{1} K_{2}}{K_{2} K_{3}}.
$$