MathDB

1

Part of 2006 India National Olympiad

Problems(1)

Non equilateral triangle $abc$ the sides $a,b,c$ form an ap

Source: Indian National Maths Olympiad, Problem 1

2/5/2006
In a non equilateral triangle ABCABC the sides a,b,ca,b,c form an arithmetic progression. Let II be the incentre and OO the circumcentre of the triangle ABCABC. Prove that (1) IOIO is perpendicular to BIBI; (2) If BIBI meets ACAC in KK, and DD, EE are the midpoints of BCBC, BABA respectively then II is the circumcentre of triangle DKEDKE.
geometryincentercircumcircletrigonometryangle bisectorsimilar trianglesgeometry proposed