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Contests
National and Regional Contests
Bosnia Herzegovina Contests
Bosnia and Herzegovina EGMO Team Selection Test
2019 Bosnia and Herzegovina EGMO TST
3
3
Part of
2019 Bosnia and Herzegovina EGMO TST
Problems
(1)
intersection of circumcircles lies on a line
Source: Bosnia and Herzegovina EGMO TST 2019 p3
8/1/2019
The circle inscribed in the triangle
A
B
C
ABC
A
BC
touches the sides
A
B
AB
A
B
and
A
C
AC
A
C
at the points
K
K
K
and
L
L
L
, respectively. The angle bisectors from
B
B
B
and
C
C
C
intersect the altitude of the triangle from the vertex
A
A
A
at the points
Q
Q
Q
and
R
R
R
, respectively. Prove that one of the points of intersection of the circles circumscribed around the triangles
B
K
Q
BKQ
B
K
Q
and
C
P
L
CPL
CP
L
lies on
B
C
BC
BC
.
geometry
circumcircle