MathDB

RMO 2012 Kar Region

Source: RMO 2012

December 16, 2012

trigonometrygeometryincentergeometry proposed

Problem Statement

Let

ABC

be a triangle. Let

BE

and

CF

be internal angle bisectors of

\angle B

and

\angle C

respectively with

E

on

AC

and

F

on

AB

. Suppose

X

is a point on the segment

CF

such that

AX

perpendicular

CF

; and

Y

is a point on the segment

BE

such that

AY

perpendicular

BE

. Prove that

XY = (b + c-a)/2

where

BC = a, CA = b

and

AB = c

.

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