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Problems
Contests
National and Regional Contests
Romania Contests
IMAR Test
2018 IMAR Test
1
1
Part of
2018 IMAR Test
Problems
(1)
IMAR Test 2018 P1
Source: IMAR Test 2018 P1
4/20/2021
Let
A
B
C
ABC
A
BC
be a triangle whose angle at
A
A
A
is right, and let
D
D
D
be the foot of the altitude from
A
A
A
. A variable point
M
M
M
traces the interior of the minor arc
A
B
AB
A
B
of the circle
A
B
C
ABC
A
BC
. The internal bisector of the angle
D
A
M
DAM
D
A
M
crosses
C
M
CM
CM
at
N
N
N
. The line through
N
N
N
and perpendicular to
C
M
CM
CM
crosses the line
A
D
AD
A
D
at
P
P
P
. Determine the locus of the point where the line
B
N
BN
BN
crosses the line
C
P
CP
CP
.* * *
geometry
Locus
romania