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2016 JBMO Shortlist
7
7
Part of
2016 JBMO Shortlist
Problems
(1)
2016 JBMO Shortlist G7
Source: 2016 JBMO Shortlist G7
10/8/2017
Let
A
B
{AB}
A
B
be a chord of a circle
(
c
)
{(c)}
(
c
)
centered at
O
{O}
O
, and let
K
{K}
K
be a point on the segment
A
B
{AB}
A
B
such that
A
K
<
B
K
{AK<BK}
A
K
<
B
K
. Two circles through
K
{K}
K
, internally tangent to
(
c
)
{(c)}
(
c
)
at
A
{A}
A
and
B
{B}
B
, respectively, meet again at
L
{L}
L
. Let
P
{P}
P
be one of the points of intersection of the line
K
L
{KL}
K
L
and the circle
(
c
)
{(c)}
(
c
)
, and let the lines
A
B
{AB}
A
B
and
L
O
{LO}
L
O
meet at
M
{M}
M
. Prove that the line
M
P
{MP}
MP
is tangent to the circle
(
c
)
{(c)}
(
c
)
.Theoklitos Paragyiou (Cyprus)
geometry
JBMO