MathDB
Problems
Contests
National and Regional Contests
The Philippines Contests
Philippine MO
2021 Philippine MO
1
1
Part of
2021 Philippine MO
Problems
(1)
geom problem
Source: PMO
3/19/2021
In convex quadrilateral
A
B
C
D
ABCD
A
BC
D
,
∠
C
A
B
=
∠
B
C
D
\angle CAB = \angle BCD
∠
C
A
B
=
∠
BC
D
.
P
P
P
lies on line
B
C
BC
BC
such that
A
P
=
P
C
AP = PC
A
P
=
PC
,
Q
Q
Q
lies on line
A
P
AP
A
P
such that
A
C
AC
A
C
and
D
Q
DQ
D
Q
are parallel,
R
R
R
is the point of intersection of lines
A
B
AB
A
B
and
C
D
CD
C
D
, and
S
S
S
is the point of intersection of lines
A
C
AC
A
C
and
Q
R
QR
QR
. Line
A
D
AD
A
D
meets the circumcircle of
A
Q
S
AQS
A
QS
again at
T
T
T
. Prove that
A
B
AB
A
B
and
Q
T
QT
QT
are parallel.
geometry
PMO