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Express MN/BC in R and r

Source: APMO 2005 Problem 5

March 23, 2005

geometrycircumcircleinradiusratioincenterEulertrigonometry

Problem Statement

In a triangle

ABC

, points

M

and

N

are on sides

AB

and

AC

, respectively, such that

MB = BC = CN

. Let

R

and

r

denote the circumradius and the inradius of the triangle

ABC

, respectively. Express the ratio

MN/BC

in terms of

R

and

r