Question 102
The circle $S_1$ intersects the hyperbola $y = \frac{1}{x}$ at four points $A$, $B$, $C$ and $D$, and the other circle $S_2$ intersects the same hyperbola at four points $A$, $B$, $F$ and $G$. It is known that the radii of circles $S_1$ and $S_2$ are equal.
Prove that the points $C$, $D$, $F$ and $G$ are the vertices of a parallelogram.
( I. Voronovich )
Prove that the points $C$, $D$, $F$ and $G$ are the vertices of a parallelogram.
( I. Voronovich )