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Baltic Way
2004 Baltic Way
18
18
Part of
2004 Baltic Way
Problems
(1)
And this is called geometry?!
Source: Baltic Way 2004 Problem 18
11/19/2004
A ray emanating from the vertex
A
A
A
of the triangle
A
B
C
ABC
A
BC
intersects the side
B
C
BC
BC
at
X
X
X
and the circumcircle of triangle
A
B
C
ABC
A
BC
at
Y
Y
Y
. Prove that
1
A
X
+
1
X
Y
≥
4
B
C
\frac{1}{AX}+\frac{1}{XY}\geq \frac{4}{BC}
A
X
1
+
X
Y
1
≥
BC
4
.
geometry
circumcircle
inequalities
geometry proposed