MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
JBMO TST - Turkey
2022 JBMO TST - Turkey
4
4
Part of
2022 JBMO TST - Turkey
Problems
(1)
Parallelity and equal angles given, wanted an angle equality
Source: 2022 Turkey JBMO TST P4
3/15/2022
Given a convex quadrilateral
A
B
C
D
ABCD
A
BC
D
such that
m
(
A
B
C
^
)
=
m
(
B
C
D
^
)
m(\widehat{ABC})=m(\widehat{BCD})
m
(
A
BC
)
=
m
(
BC
D
)
. The lines
A
D
AD
A
D
and
B
C
BC
BC
intersect at a point
P
P
P
and the line passing through
P
P
P
which is parallel to
A
B
AB
A
B
, intersects
B
D
BD
B
D
at
T
T
T
. Prove that
m
(
A
C
B
^
)
=
m
(
P
C
T
^
)
m(\widehat{ACB})=m(\widehat{PCT})
m
(
A
CB
)
=
m
(
PCT
)
geometry
Parallel Lines
Angle condition