On the Area of Pedal and Antipedal Triangles

2010/07/28 by Mitrea, Adrian
#51M15 #51M16. Secondary 51M04 #51N20 #FOS: Mathematics #Metric Geometry (math.MG) #Primary: 51M25

paper · doi:10.48550/arxiv.1008.0110

Abstract

We give a new proof of the formula expressing the area of the triangle whose vertices are the projections of an arbitrary point in the plane onto the sides of a given triangle, in terms of the geometry of the given triangle and the location of the projection point. Other related geometrical constructions and formulas are also presented.

Related

• Points, whose pedal triangles are similar to the given triangle
• Topics on Pedal Polygons
• Area of triangles associated with a curve
• Areas of triangles and SL₂ actions in finite rings
• Area-Invariant Pedal-Like Curves Derived from the Ellipse