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Poland Contests
Poland - Second Round
1983 Poland - Second Round
5
5
Part of
1983 Poland - Second Round
Problems
(1)
AK+BL+CM > AB+BC+CA
Source: Polish MO Recond Round 1983 p5
9/9/2024
The bisectors of the angles
C
A
B
,
A
B
C
,
B
C
A
CAB, ABC, BCA
C
A
B
,
A
BC
,
BC
A
of the triangle
A
B
C
ABC
A
BC
intersect the circle circumcribed around this triangle at points
K
,
L
,
M
K, L, M
K
,
L
,
M
, respectively. Prove that
A
K
+
B
L
+
C
M
>
A
B
+
B
C
+
C
A
.
AK+BL+CM > AB+BC+CA.
A
K
+
B
L
+
CM
>
A
B
+
BC
+
C
A
.
geometry
Geometric Inequalities