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Germany Contests
German National Olympiad
2021 German National Olympiad
4
4
Part of
2021 German National Olympiad
Problems
(1)
Two similar triangles and a parallelogram called FANO
Source: Germany 2021, Problem 4
6/16/2021
Let
O
F
T
OFT
OFT
and
N
O
T
NOT
NOT
be two similar triangles (with the same orientation) and let
F
A
N
O
FANO
F
A
NO
be a parallelogram. Show that
∣
O
F
∣
⋅
∣
O
N
∣
=
∣
O
A
∣
⋅
∣
O
T
∣
.
\vert OF\vert \cdot \vert ON\vert=\vert OA\vert \cdot \vert OT\vert.
∣
OF
∣
⋅
∣
ON
∣
=
∣
O
A
∣
⋅
∣
OT
∣.
geometry
similar triangles
parallelogram
geometry proposed
lengths