# How to prove it

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

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## Abstract

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 |
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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 |

Depositing User: | Mr. Sachin Tirlapur |

Date Deposited: | 25 Oct 2018 14:17 |

Last Modified: | 29 Jul 2019 07:07 |

URI: | http://publications.azimpremjifoundation.org/id/eprint/1575 |

Publisher URL: | http://apfstatic.s3.ap-south-1.amazonaws.com/s3fs-... |

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