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National and Regional Contests
China Contests
China Northern MO
2009 China Northern MO
6
6
Part of
2009 China Northern MO
Problems
(1)
area of polygon AQPBO does not change when points P,C move
Source: China Northern MO 2009 p6 CNMO
12/12/2020
Given a minor sector
A
O
B
AOB
A
OB
(Here minor means that
∠
A
O
B
<
90
\angle AOB <90
∠
A
OB
<
90
).
O
O
O
is the centre , chose a point
C
C
C
on arc
A
B
AB
A
B
,Let
P
P
P
be a point on segment
O
C
OC
OC
, join
A
P
AP
A
P
,
B
P
BP
BP
, draw a line through
B
B
B
parallel to
A
P
AP
A
P
, the line meet
O
C
OC
OC
at point
Q
Q
Q
,join
A
Q
AQ
A
Q
. Prove that the area of polygon
A
Q
P
B
O
AQPBO
A
QPBO
does not change when points
P
,
C
P,C
P
,
C
move . https://cdn.artofproblemsolving.com/attachments/3/e/4bdd3a20fe1df3fce0719463b55ef93e8b5d7b.png
geometry
fixed
area