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National and Regional Contests
France Contests
France Team Selection Test
2004 France Team Selection Test
2
2
Part of
2004 France Team Selection Test
Problems
(1)
Inequality for the incircle
Source: French TST 2004, pb. 5; 16th KMO #4
5/25/2004
Let
P
P
P
,
Q
Q
Q
, and
R
R
R
be the points where the incircle of a triangle
A
B
C
ABC
A
BC
touches the sides
A
B
AB
A
B
,
B
C
BC
BC
, and
C
A
CA
C
A
, respectively. Prove the inequality
B
C
P
Q
+
C
A
Q
R
+
A
B
R
P
≥
6
\frac{BC} {PQ} + \frac{CA} {QR} + \frac{AB} {RP} \geq 6
PQ
BC
+
QR
C
A
+
RP
A
B
≥
6
.
inequalities
geometry
incenter
trigonometry
inradius
perimeter
cyclic quadrilateral