olymmath

RMO 2012

Indian Regional Mathematical Olympiad 2012.

Official paper

The official paper in 5 languages

English (mumbai) · English (paper1) · English (paper2) · English (paper3) · English (paper4)

CRMO Paper 1

A5

  • CRMO Paper 1

Let ABCABC be a triangle. Let BEBE and CFCF be internal angle bisectors of ∠B\angle B and ∠C\angle C respectively with EE on ACAC and FF on ABAB . Suppose XX is a point on the segment CFCF such that AXAX perpendicular CFCF ; and YY is a point on the segment BEBE such that AYAY perpendicular BEBE . Prove that XY=(b+c−a)/2XY = (b + c-a)/2 where BC=a,CA=bBC = a, CA = b and AB=cAB = c .

Answer, solutions and source

CRMO Paper 2

CRMO Paper 3

CRMO Paper 4

Mumbai Region