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2015 JBMO Shortlist
3
3
Part of
2015 JBMO Shortlist
Problems
(1)
2015 JBMO Shortlist G3
Source: 2015 JBMO Shortlist G3
10/8/2017
Let
c
≡
c
(
O
,
R
)
{c\equiv c\left(O, R\right)}
c
≡
c
(
O
,
R
)
be a circle with center
O
{O}
O
and radius
R
{R}
R
and
A
,
B
{A, B}
A
,
B
be two points on it, not belonging to the same diameter. The bisector of angle
∠
A
B
O
{\angle{ABO}}
∠
A
BO
intersects the circle
c
{c}
c
at point
C
{C}
C
, the circumcircle of the triangle
A
O
B
AOB
A
OB
, say
c
1
{c_1}
c
1
at point
K
{K}
K
and the circumcircle of the triangle
A
O
C
AOC
A
OC
, say
c
2
{{c}_{2}}
c
2
at point
L
{L}
L
. Prove that point
K
{K}
K
is the circumcircle of the triangle
A
O
C
AOC
A
OC
and that point
L
{L}
L
is the incenter of the triangle
A
O
B
AOB
A
OB
.Evangelos Psychas (Greece)
geometry
JBMO