MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - Other Middle and High School Contests
CNCM Online
CNCM Online Round 2
7
7
Part of
CNCM Online Round 2
Problems
(1)
CNCM Online R2P7
Source:
8/8/2020
A circle is centered at point
O
O
O
in the plane. Distinct pairs of points
A
,
B
A, B
A
,
B
and
C
,
D
C, D
C
,
D
are diametrically opposite on this circle. Point
P
P
P
is chosen on line segment
A
D
AD
A
D
such that line
B
P
BP
BP
hits the circle again at
M
M
M
and line
A
C
AC
A
C
at
X
X
X
such that
M
M
M
is the midpoint of
P
X
PX
PX
. Now, the point
Y
≠
X
Y \neq X
Y
=
X
is taken for
B
X
=
B
Y
,
C
D
∥
X
Y
BX = BY, CD \parallel XY
BX
=
B
Y
,
C
D
∥
X
Y
. IF
∠
P
Y
B
=
1
0
∘
\angle PYB = 10^{\circ}
∠
P
Y
B
=
1
0
∘
, find the measure of
∠
X
C
M
\angle XCM
∠
XCM
. Proposed by Albert Wang (awang11)
CNCM
Problem Discussion