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Acute triangle and semicircle with diameter AC

Source: Cono Sur 2003 #3

November 18, 2015

geometrycono sur

Problem Statement

Let

ABC

be an acute triangle such that

\angle{B}=60

. The circle with diameter

AC

intersects the internal angle bisectors of

A

and

C

at the points

M

and

N

, respectively

(M\neq{A},

N\neq{C})

. The internal bisector of

\angle{B}

intersects

MN

and

AC

at the points

R

and

S

, respectively. Prove that

BR\leq{RS}

.

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