MathDB

Everything is integer

Source: Hungary

July 1, 2020

geometry

Problem Statement

Let

T

be any triangle such that its side-lengths

a, b

and

c

and its circumradius

R

are positive integers. Show that: a) the inradius

r

of

T

is a positive integer; b) the perimeter

P

of

T

is a multiple of

4

; and c) all three of

a, b

and

c

are even.

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