Question 5
The sphere $\omega$ passes through vertex $S$ of the pyramid $SABC$ and meets edges $SA$, $SB$ and $SC$ a second time at $A_1$, $B_1$ and $C_1$, respectively. The sphere $\Omega$ circumscribed about $SABC$ intersects $\omega$ in a circle whose plane is parallel to $(ABC)$. Points $A_2$, $B_2$ and $C_2$ are the reflections of $A_1$, $B_1$ and $C_1$ in the midpoints of $SA$, $SB$ and $SC$, respectively. Prove that $A,B,C,A_2,B_2,C_2$ lie on one sphere. (I. Bogdanov)