On the Area of Pedal and Antipedal Triangles

TL;DR

This paper presents a new proof for the area formula of pedal triangles, relating the area to the original triangle's geometry and the projection point, along with additional related geometric formulas.

Contribution

It introduces a novel proof for the pedal triangle area formula and explores related geometric constructions and formulas.

Findings

New proof of the pedal triangle area formula

Derived additional geometric constructions and formulas

Enhanced understanding of projections in triangle geometry

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.