Four Concyclic Points
Let ABC be a triangle and H the foot of the altitude from B. Let M be the midpoint of AC. Let P and Q be the feet of the perpendiculars from A and C to the angle bisector of the angle ABC. Then H, M, P and Q lie on a circle.
Contributed by:
Jay Warendorff
After work by:
D. Grinberg
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D. Grinberg, "From Baltic Way to Feuerbach: A Geometrical Excursion,"
Mathematical Refections
[
online
] (2), 2000 p. 2.
Circle
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Wolfram
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Concyclic
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Wolfram
MathWorld
)
"
Four Concyclic Points
" from
The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/FourConcyclicPoints/
Contributed by:
Jay Warendorff
After work by:
D. Grinberg
High School Geometry
Plane Geometry
Triangles
Inscribing Four Circles in a Triangle
Nine-Point Circle
Division of the Opposite Side by an Angle Bisector
Angle Bisectors in a Triangle
The Perpendicular Bisectors of a Triangle
Triangle Altitudes and Circumradius
Triangle Altitudes and Inradius
The Area of a Triangle as Half a Rectangle
Napoleon's Theorem
Dividing a Right Triangle by the Altitude to the Hypotenuse
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