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Lusophon Mathematical Olympiad
2014 Lusophon Mathematical Olympiad
4
4
Part of
2014 Lusophon Mathematical Olympiad
Problems
(1)
IV Lusophon Mathematical Olympiad 2014 - Problem 4
Source:
12/28/2014
From a point
K
K
K
of a circle, a chord
K
A
KA
K
A
(arc
A
K
AK
A
K
is greather than
9
0
o
90^{o}
9
0
o
) and a tangent
l
l
l
are drawn. The line that passes through the center of the circle and that is perpendicular to the radius
O
A
OA
O
A
, intersects
K
A
KA
K
A
at
B
B
B
and
l
l
l
at
C
C
C
. Show that
K
C
=
B
C
KC = BC
K
C
=
BC
.