Question 106
The points $X, Y, Z$ are in this order on a straight line with $|X Y| \neq |Y Z|$. Be $k_{1}$ or $k_{2}$ the circle with diameter $X Y$ or $Y Z$. The points $A_{1}$ and $B_{1}$ or $A_{2}$ and $B_{2}$ are on $k_{1}$ or $k_{2}$, so $$
\angle A_{1} Y A_{2} = \angle B_{1} Y B_{2} = 90^{\circ}
$$ applies. Show that the two straight lines $A_{1} A_{2}$ and $B_{1} B_{2}$ intersect on $X Y$.
\angle A_{1} Y A_{2} = \angle B_{1} Y B_{2} = 90^{\circ}
$$ applies. Show that the two straight lines $A_{1} A_{2}$ and $B_{1} B_{2}$ intersect on $X Y$.