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KoMaL A Problems
KoMaL A Problems 2019/2020
A. 766
A. 766
Part of
KoMaL A Problems 2019/2020
Problems
(1)
Everything is integer
Source: Hungary
7/1/2020
Let
T
T
T
be any triangle such that its side-lengths
a
,
b
a, b
a
,
b
and
c
c
c
and its circumradius
R
R
R
are positive integers. Show that: a) the inradius
r
r
r
of
T
T
T
is a positive integer; b) the perimeter
P
P
P
of
T
T
T
is a multiple of
4
4
4
; and c) all three of
a
,
b
a, b
a
,
b
and
c
c
c
are even.
geometry