S must be the incentre of triangle ABC
Source: Baltic Way 2007
November 30, 2010
geometryincentercircumcircletrigonometrygeometry proposed
Problem Statement
In triangle let and be the altitudes. Let the points and fulfil the following requirements:
i) is the circumcentre of triangle .
ii) All the segments and are equal to the circumradius of triangle .
iii) The oriented segment has the same direction as the oriented segment . Similarly, has the same direction as , and has the same direction as .
Prove that is the incentre of triangle .