Miraj, Rahil
(2019)
Radii of incircle and excircles of a right angled triangle.
At Right Angles (4).
pp. 2730.
ISSN 25821873
Abstract
In this article, I provide a relation connecting the lengths of the tangents from the vertices of a rightangled triangle to its incircle and excircles, in terms of its inradius and exradii. I give a geometric proof as well as an analytic proof.
A standard result which will be used repeatedly is the following: Given a circle and a point outside it, the lengths of the two tangents that can be drawn from the point to the circle have equal length. A list of more such results and formulas of relevance is provided at the end of the article. The following nomenclature should be noted. Other than the incircle of a triangle, three other circles can be drawn that touch the sidelines of a triangle. These are called the excircles of the triangle. The excircle opposite vertex A is known as the ‘A excircle’, and likewise for the two other excircles. The radius ra of the A excircle is called the ‘A exradius’, and similarly for the radii of the two other excircles.
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