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Indonesia Regional
Indonesia Regional MO OSP SMA - geometry
2009.3
2009.3
Part of
Indonesia Regional MO OSP SMA - geometry
Problems
(1)
r_1 + r_2> r, inradii
Source: 2009 Indonedia MO Province P2 q3 OSP
12/11/2020
Given triangle
A
B
C
ABC
A
BC
and point
D
D
D
on the
A
C
AC
A
C
side. Let
r
1
,
r
2
r_1, r_2
r
1
,
r
2
and
r
r
r
denote the radii of the incircle of the triangles
A
B
D
,
B
C
D
ABD, BCD
A
B
D
,
BC
D
, and
A
B
C
ABC
A
BC
, respectively. Prove that
r
1
+
r
2
>
r
r_1 + r_2> r
r
1
+
r
2
>
r
.
geometry
geometric inequality