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China Northern MO
2013 China Northern MO
6
6
Part of
2013 China Northern MO
Problems
(1)
PO _|_BC wanted, circle passing thorugh A,C and tangent to median AM
Source: China Northern MO 2013 p6 CNMO
10/28/2022
As shown in figure , it is known that
M
M
M
is the midpoint of side
B
C
BC
BC
of
△
A
B
C
\vartriangle ABC
△
A
BC
.
⊙
O
\odot O
⊙
O
passes through points
A
,
C
A, C
A
,
C
and is tangent to
A
M
AM
A
M
. The extension of the segment
B
A
BA
B
A
intersects
⊙
O
\odot O
⊙
O
at point
D
D
D
. The lines
C
D
CD
C
D
and
M
A
MA
M
A
intersect at the point
P
P
P
. Prove that
P
O
⊥
B
C
PO \perp BC
PO
⊥
BC
. https://cdn.artofproblemsolving.com/attachments/8/a/da3570ec7eb0833c7a396e22ffac2bd8902186.png
perpendicular
geometry