Fontené Theorems
- 1. If the sides of the Pedal Triangle of a point
meet the corresponding sides of a Triangle
at 
, 
, and 
, respectively, then 
, 
, 
meet at a point 
common to the Circles 
and 
. In other words, is one of the intersectionsof the Nine-Point Circle of 
and the Pedal Circle of . - 2. If a point moves on a fixed line through the Circumcenter, then its Pedal Circle passesthrough a fixed point on the Nine-Point Circle.
- 3. The Pedal Circle of a point is tangent to the Nine-Point Circle Iff the point and itsIsogonal Conjugate lie on a Line through the Orthocenter. Feuerbach's Theorem is a special case of this theorem.
References
Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, pp. 245-247, 1929.
- Rectification
- Rectifying Latitude
- Rectifying Plane
- Recurrence Relation
- Recurrence Sequence
- Recurring Digital Invariant
- Recursion
- Recursive Function
- Recursive Monotone Stable Quadrature
- Red-Black Tree
- Red Net
- Reduced Amicable Pair
- Reduced Fraction
- Reduced Latitude
- Reducible Crossing
- Reducible Matrix
- Reducible Representation
- Reduction of Order
- Reduction Theorem
- Redundancy
- Reeb Foliation
- Reef Knot
- Re-Entrant Circuit
- Refinement
- Reflection