411 REFERENCE · Wikibooks
Trigonometry/Reflections in a triangle
Reference material by Wikibooks contributors. This retains its source identity and is not 411 news reporting.
Take any triangle ABC and any point P.
Let X be the reflection of P in BC (or BC extended), Y be the reflection of P in AC (or AC extended) and Z be the reflection of P in AB (or AB extended).
Then the four circles XYC, YZA, ZXB and the circumcircle of ABC all paas through the same point, the reflection of P in ABC.