How to prove it

Shirali, Shailesh (2018) How to prove it. At Right Angles, 7 (2). pp. 95-100. ISSN 2582-1873

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Euler’s formula for the area of a pedal triangle Given a triangle ABC and a point P in the plane of ABC (note that P does not have to lie within the triangle), the pedal triangle of P with respect to △ ABC is the triangle whose vertices are the feet of the perpendiculars drawn from P to the sides of ABC. See Figure 1. The pedal triangle relates in a natural way to the parent triangle, and we may wonder whether there is a convenient formula giving the area of the pedal triangle in terms of the parameters of the parent triangle. The great 18th-century mathematician Euler found just such a formula (given in Box 1). It is a compact and pleasing result, and it expresses the area of the pedal triangle in terms of the radius R of the circumcircle of △ ABC and the distance between P and the centre O of the circumcircle.

Item Type: Articles in APF Magazines
Authors: Shirali, Shailesh
Document Language:
Uncontrolled Keywords: Circle theorem, pedal triangle, power of a point, Euler, sine rule, extended sine rule, Wallace-Simson theorem
Subjects: Natural Sciences > Mathematics
Divisions: Azim Premji University > University Publications > At Right Angles
Full Text Status: Public
Publisher URL:

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