An Altitude and Four Concyclic Points


	Let ABC be a triangle and let A' be the foot of the altitude from A. Let P and Q be the perpendicular projections of A' onto AB and AC, respectively. Then B, C, P, and Q are concyclic.


	Contributed by: Jay Warendorff

Altitude (Wolfram MathWorld)

Concyclic (Wolfram MathWorld)

Perpendicular (Wolfram MathWorld)

"An Altitude and Four Concyclic Points" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/AnAltitudeAndFourConcyclicPoints/

Contributed by: Jay Warendorff

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Plane Geometry
Triangles

Browse all topics

Four Concyclic Points
Concyclic Points Derived from Midpoints of Altitudes
Four Collinear Points Related to the Altitudes
Concyclic Points Related to a Midpoint and the Incircle
Three Concyclic Sets of Points Associated with the Orthic Triangle
A Relation between Altitudes of Four Triangles
Concyclic Circumcenters
A Collinearity between the Nine-Point Center, the Foot of an Altitude, and a Midpoint
Projections, an Altitude, and the Orthocenter
Dividing a Right Triangle by the Altitude to the Hypotenuse

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