# Inscribing a triangle in a circle in spherical geometry

### Himalaya Senapati

Chennai Mathematical Institute, Siruseri, India

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## Abstract

We consider the geometrical problem of constructing a triangle using a straightedge and compass so that its three vertices lie on a given circle and its three sides when produced pass through three given points. This problem was formulated and studied by Pappus of Alexandria in his *Collection* in the special case where the three given points are aligned (Proposition 117 of Book VII of the *Collection*). Lagrange gave an algebraic solution to this problem (1776). Euler gave another solution and commented on the case where the given circle and the three given points are on a sphere (1780). In this chapter, after recalling the solution due to Lagrange, we study the same problem on the sphere.