MathDB
Problems
Contests
National and Regional Contests
India Contests
India IMO Training Camp
2024 India IMOTC
22
22
Part of
2024 India IMOTC
Problems
(1)
60 deg strikes again
Source: LMAO 2024 P4
6/1/2024
Let
A
B
C
ABC
A
BC
be a triangle with circumcenter
O
O
O
and
∠
B
A
C
=
6
0
∘
\angle BAC = 60^{\circ}
∠
B
A
C
=
6
0
∘
. The internal angle bisector of
∠
B
A
C
\angle BAC
∠
B
A
C
meets line
B
C
BC
BC
and the circumcircle of
△
A
B
C
\triangle ABC
△
A
BC
in points
M
,
L
M,L
M
,
L
respectively. Let
K
K
K
denote the reflection of
B
L
∩
A
C
BL\cap AC
B
L
∩
A
C
over the line
B
C
BC
BC
. Let
D
D
D
be on the line
C
O
CO
CO
with
D
M
DM
D
M
perpendicular to
K
L
KL
K
L
. Prove that points
K
,
A
,
D
K,A,D
K
,
A
,
D
are collinear.Proposed by Sanjana Philo Chacko
geometry
lmao
LMAO Mock