Question 2
The circles $\omega_1$ and $\omega_2$ centered at $O_1$ and $O_2$, respectively, intersect at two different points $E$ and $F$. The line $O_1E$ intersects for the second time $\omega_1$ at the point $A$, and $\omega_2$ at the point $C$. The line $O_2E$ intersects for the second time $\omega_2$ at the point $B$, and $\omega_1$ at the point $D$.
Prove that the perpendiculars to the lines $AC, BD$ and $DC$, passing through $O_1, O_2$ and $E$, respectively, are concurrent.
(A. Voidelevich)
Prove that the perpendiculars to the lines $AC, BD$ and $DC$, passing through $O_1, O_2$ and $E$, respectively, are concurrent.
(A. Voidelevich)