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triangle with b+c=2a

Source: 2005 Spanish Mathematical Olympiad P6

July 20, 2018

geometryinradiuscircumradiusSides of a triangle

Problem Statement

In a triangle with sides

a, b, c

the side

a

is the arithmetic mean of

b

and

c

. Prove that: a)

0^o \le A \le 60^o

. b) The height relative to side

a

is three times the inradius

r

. c) The distance from the circumcenter to side

a

is

R - r

, where

R

is the circumradius.

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