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National and Regional Contests
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Singapore Senior Math Olympiad
2017 Singapore Senior Math Olympiad
2
2
Part of
2017 Singapore Senior Math Olympiad
Problems
(1)
right angle leads to right angle, intersections of sides of cyclic ABCD related
Source: 2017 Singapore Seniors Round 2 p2
3/18/2020
In the cyclic quadrilateral
A
B
C
D
ABCD
A
BC
D
, the sides
A
B
,
D
C
AB, DC
A
B
,
D
C
meet at
Q
Q
Q
, the sides
A
D
,
B
C
AD,BC
A
D
,
BC
meet at
P
,
M
P, M
P
,
M
is the midpoint of
B
D
BD
B
D
, If
∠
A
P
Q
=
9
0
o
\angle APQ=90^o
∠
A
PQ
=
9
0
o
, prove that
P
M
PM
PM
is perpendicular to
A
B
AB
A
B
.
geometry
right angle
perpendicular
cyclic quadrilateral
Cyclic