Editing Pedal triangle (section)

== Pedal circle ==
{{Main|Pedal circle}}
[[File:Isogonal points2 pedal circle.svg|thumb|336x336px|The pedal circle of the point {{mvar|P}} and its isogonal conjugate {{mvar|P*}} are the same.]]
The pedal circle is defined as the [[circumcircle]] of the pedal triangle. Note that the pedal circle is not defined for points lying on the circumcircle of the triangle. 

=== Pedal circle of isogonal conjugates ===
For any point {{mvar|P}} not lying on the circumcircle of the triangle, it is known that {{mvar|P}} and its [[isogonal conjugate]] {{mvar|P*}} have a common pedal circle, whose center is the midpoint of these two points.<ref>{{Cite book|last=Honsberger|first=Ross|url=http://dx.doi.org/10.5948/upo9780883859513|title=Episodes in Nineteenth and Twentieth Century Euclidean Geometry|date=1995-01-01|publisher=The Mathematical Association of America|isbn=978-0-88385-951-3}}</ref>