Intercept theorem/Three rays/Fact/Proof

Proof

We apply fact twice, to the situation given by $s_1,s_2$ and to the situation given by $s_2,s_3$, and we obtain

$\frac{d(B_1,B_2)}{d(A_1,A_2)}=\frac{\Vert B_2\Vert }{\Vert A_2\Vert }=\frac{d(B_2,B_3)}{d(A_2,A_3)}.$

To fact