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Contests
National and Regional Contests
Switzerland Contests
Swiss NMO - geometry
2022.1
2022.1
Part of
Swiss NMO - geometry
Problems
(1)
BX/XD=? AB diameter of circle , AC = AM, CD = AB
Source: Switzerland - 2022 Swiss Final Round p1
11/17/2022
Let
k
k
k
be a circle with centre
M
M
M
and let
A
B
AB
A
B
be a diameter of
k
k
k
. Furthermore, let
C
C
C
be a point on
k
k
k
such that
A
C
=
A
M
AC = AM
A
C
=
A
M
. Let
D
D
D
be the point on the line
A
C
AC
A
C
such that
C
D
=
A
B
CD = AB
C
D
=
A
B
and
C
C
C
lies between
A
A
A
and
D
D
D
. Let
E
E
E
be the second intersection of the circumcircle of
B
C
D
BCD
BC
D
with line
A
B
AB
A
B
and
F
F
F
be the intersection of the lines
E
D
ED
E
D
and
B
C
BC
BC
. The line
A
F
AF
A
F
cuts the segment
B
D
BD
B
D
in
X
X
X
. Determine the ratio
B
X
/
X
D
BX/XD
BX
/
X
D
.
ratio
geometry