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National and Regional Contests
Saudi Arabia Contests
Saudi Arabia Pre-TST + Training Tests
2015 Saudi Arabia Pre-TST
2.1
2.1
Part of
2015 Saudi Arabia Pre-TST
Problems
(1)
A and circumcenters of ABC, DEF are collinear
Source: 2015 Saudi Arabia Pre-TST 2.1
9/12/2020
Let
A
B
C
ABC
A
BC
be a triangle and
D
D
D
a point on the side
B
C
BC
BC
. The tangent line to the circumcircle of the triangle
A
B
D
ABD
A
B
D
at the point
D
D
D
intersects the side
A
C
AC
A
C
at
E
E
E
. The tangent line to the circumcircle of the triangle
A
C
D
ACD
A
C
D
at the the point
D
D
D
intersects the side
A
B
AB
A
B
at
F
F
F
. Prove that the point
A
A
A
and the circumcenters of the triangles
A
B
C
ABC
A
BC
and
D
E
F
DEF
D
EF
are collinear.(Malik Talbi)
geometry
circumcircle