Non equilateral triangle $abc$ the sides $a,b,c$ form an ap
Source: Indian National Maths Olympiad, Problem 1
February 5, 2006
geometryincentercircumcircletrigonometryangle bisectorsimilar trianglesgeometry proposed
Problem Statement
In a non equilateral triangle the sides form an arithmetic progression. Let be the incentre and the circumcentre of the triangle . Prove that
(1) is perpendicular to ;
(2) If meets in , and , are the midpoints of , respectively then is the circumcentre of triangle .