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Contests
National and Regional Contests
Ukraine Contests
Official Ukraine Selection Cycle
Kyiv City MO
Kyiv City MO - geometry
Kyiv City MO Juniors 2003+ geometry
2004.9.7
2004.9.7
Part of
Kyiv City MO Juniors 2003+ geometry
Problems
(1)
triangle construction given 3 points (Kyiv City Olympiad 2004 9.7)
Source:
6/27/2021
The board depicts the triangle
A
B
C
ABC
A
BC
, the altitude
A
H
AH
A
H
and the angle bisector
A
L
AL
A
L
which intersectthe inscribed circle in the triangle at the points
M
M
M
and
N
,
P
N, P
N
,
P
and
Q
Q
Q
, respectively. After that, the figure was erased, leaving only the points
H
,
M
H, M
H
,
M
and
Q
Q
Q
. Restore the triangle
A
B
C
ABC
A
BC
.(Bogdan Rublev)
geometry
construction