Asked by Dillion
                Let A and B be two points on the hyperbola xy=1, and let C be the reflection of B through the origin.
Let Gamma be the circumcircle of triangle ABC and let A' be the point on Gamma diametrically opposite A. Show that A' is also on the hyperbola xy=1.
            
        Let Gamma be the circumcircle of triangle ABC and let A' be the point on Gamma diametrically opposite A. Show that A' is also on the hyperbola xy=1.
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