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Geometry Mathley 2011-12
5.2
5.2
Part of
Geometry Mathley 2011-12
Problems
(1)
Geometry Mathley 5.2 1/ PQ^2 >= 1/ UV^2 - / AC^2
Source:
6/7/2020
Let
A
B
C
D
ABCD
A
BC
D
be a rectangle and
U
,
V
U, V
U
,
V
two points of its circumcircle. Lines
A
U
,
C
V
AU,CV
A
U
,
C
V
intersect at
P
P
P
and lines
B
U
,
D
V
BU,DV
B
U
,
D
V
intersect at
Q
Q
Q
, distinct from
P
P
P
. Prove that
1
P
Q
2
≥
1
U
V
2
−
1
A
C
2
\frac{1}{PQ^2} \ge \frac{1}{UV^2} - \frac{1}{AC^2}
P
Q
2
1
≥
U
V
2
1
−
A
C
2
1
Michel Bataille
rectangle
geometry
geometric inequality
circumcircle