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Moldova Contests
Moldova Team Selection Test
1999 Moldova Team Selection Test
4
4
Part of
1999 Moldova Team Selection Test
Problems
(1)
perpendiculars form $A, B$ and $C$ on $(EF), (FD)$ and $(DE)$ are concurrent
Source: Moldova TST 1999
8/7/2023
Outside the triangle
A
B
C
ABC
A
BC
the isosceles triangles
A
F
B
,
B
D
C
AFB, BDC
A
FB
,
B
D
C
and
C
E
A
CEA
CE
A
with the bases
A
B
,
B
C
AB, BC
A
B
,
BC
and
C
A
CA
C
A
respectively, are constructed. Show that the perpendiculars form
A
,
B
A, B
A
,
B
and
C
C
C
on
(
E
F
)
,
(
F
D
)
(EF), (FD)
(
EF
)
,
(
F
D
)
and
(
D
E
)
(DE)
(
D
E
)
, respectively, are concurrent.
geometry