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2022 Silk Road
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Part of
2022 Silk Road
Problems
(1)
Geometry Problem
Source: SRMC 2022 P1
5/23/2022
Convex quadrilateral
A
B
C
D
ABCD
A
BC
D
is inscribed in circle
w
.
w.
w
.
Rays
A
B
AB
A
B
and
D
C
DC
D
C
intersect at
K
.
L
K.\ L
K
.
L
is chosen on the diagonal
B
D
BD
B
D
so that
∠
B
A
C
=
∠
D
A
L
.
M
\angle BAC= \angle DAL.\ M
∠
B
A
C
=
∠
D
A
L
.
M
is chosen on the segment
K
L
KL
K
L
so that
C
M
∣
∣
B
D
.
CM \mid\mid BD.
CM
∣∣
B
D
.
Prove that line
B
M
BM
BM
touches
w
.
w.
w
.
(Kungozhin M.)
geometry