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Contests
National and Regional Contests
Russia Contests
All-Russian Olympiad Regional Round
2009 All-Russian Olympiad Regional Round
11.6
11.6
Part of
2009 All-Russian Olympiad Regional Round
Problems
(1)
CL= BC if AB=AD
Source: All-Russian MO 2009 Regional 11.6
8/27/2024
Point
D
D
D
on side
B
C
BC
BC
of acute triangle ABC is such that
A
B
=
A
D
AB=AD
A
B
=
A
D
. The circumcircle of triangle
A
B
D
ABD
A
B
D
intersects side
A
C
AC
A
C
at points
A
A
A
and
K
K
K
. Line
D
K
DK
DK
intersects the perpendicular drawn from
B
B
B
on
A
C
AC
A
C
, at the point
L
L
L
. Prove that
C
L
=
B
C
CL= BC
C
L
=
BC
geometry
equal segments