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Contests
National and Regional Contests
Belgium Contests
Flanders Math Olympiad
2023 Flanders Math Olympiad
2
2
Part of
2023 Flanders Math Olympiad
Problems
(1)
equal circles wanted
Source: 2023 Belgium, VWO Flanders MO p2
3/25/2024
In the plane, the point
M
M
M
is the midpoint of a line segment
[
A
B
]
[AB]
[
A
B
]
and
ℓ
\ell
ℓ
is an arbitrary line that has no has a common point with the line segment
[
A
B
]
[AB]
[
A
B
]
(and is also not perpendicular to
[
A
B
]
[AB]
[
A
B
]
). The points
X
X
X
and
Y
Y
Y
are the perpendicular projections of
A
A
A
and
B
B
B
onto
ℓ
\ell
ℓ
, respectively. Show that the circumscribed circles of triangle
△
A
M
X
\vartriangle AMX
△
A
MX
and triangle
△
B
M
Y
\vartriangle BMY
△
BM
Y
have the same radius.
geometry
equal circles