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Problems
Contests
National and Regional Contests
Ukraine Contests
Official Ukraine Selection Cycle
Ukraine Team Selection Test
1999 Ukraine Team Selection Test
1
1
Part of
1999 Ukraine Team Selection Test
Problems
(1)
locus of intersection of perpendicular lines, cyclic given
Source: Ukrainian TST 1999 p1
2/13/2020
A triangle
A
B
C
ABC
A
BC
is given. Points
E
,
F
,
G
E,F,G
E
,
F
,
G
are arbitrarily selected on the sides
A
B
,
B
C
,
C
A
AB,BC,CA
A
B
,
BC
,
C
A
, respectively, such that
A
F
⊥
E
G
AF\perp EG
A
F
⊥
EG
and the quadrilateral
A
E
F
G
AEFG
A
EFG
is cyclic. Find the locus of the intersection point of
A
F
AF
A
F
and
E
G
EG
EG
.
geometry
Locus
perpendicular
Cyclic