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Greece Contests
Greece Junior Math Olympiad
2018 Greece Junior Math Olympiad
4
4
Part of
2018 Greece Junior Math Olympiad
Problems
(1)
Circles are tangent
Source: Greece JMO 2018, pr 4
3/5/2018
Let
A
B
C
ABC
A
BC
with
A
B
<
A
C
<
B
C
AB<AC<BC
A
B
<
A
C
<
BC
be an acute angled triangle and
c
c
c
its circumcircle. Let
D
D
D
be the point diametrically opposite to
A
A
A
. Point
K
K
K
is on
B
D
BD
B
D
such that
K
B
=
K
C
KB=KC
K
B
=
K
C
. The circle
(
K
,
K
C
)
(K, KC)
(
K
,
K
C
)
intersects
A
C
AC
A
C
at point
E
E
E
. Prove that the circle
(
B
K
E
)
(BKE)
(
B
K
E
)
is tangent to
c
c
c
.
geometry
tangent circles