MathDB
Problems
Contests
National and Regional Contests
Korea Contests
Korea Junior Mathematics Olympiad
2000 Korea Junior Math Olympiad
3
3
Part of
2000 Korea Junior Math Olympiad
Problems
(1)
KJMO 2000 P3 AD, BQ, CR meet at one point
Source: KJMO 2000
6/29/2024
Acute triangle
A
B
C
ABC
A
BC
is inscribed in circle
O
O
O
.
P
P
P
is the foot of altitude from
A
A
A
to
B
C
BC
BC
, and
D
D
D
is the intersection of
O
O
O
and line
A
P
AP
A
P
.
M
,
N
M, N
M
,
N
are midpoint of
A
B
,
A
C
AB, AC
A
B
,
A
C
respectively.
M
P
MP
MP
and
C
D
CD
C
D
intersects at
Q
Q
Q
, and
N
P
NP
NP
and
B
D
BD
B
D
intersects at
R
R
R
. Show that
A
D
,
B
Q
,
C
R
AD, BQ, CR
A
D
,
BQ
,
CR
meet at one point if and only if
A
B
=
A
C
AB=AC
A
B
=
A
C
.
geometry
KJMO