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National and Regional Contests
Germany Contests
German National Olympiad
2014 German National Olympiad
6
6
Part of
2014 German National Olympiad
Problems
(1)
Angles in a circumscribed quadrilateral.
Source: Germany 2014 - Problem 6
12/4/2022
Let
A
B
C
D
ABCD
A
BC
D
be a circumscribed quadrilateral and
M
M
M
the centre of the incircle. There are points
P
P
P
and
Q
Q
Q
on the lines
M
A
MA
M
A
and
M
C
MC
MC
such that
∠
C
B
A
=
2
∠
Q
B
P
.
\angle CBA= 2\angle QBP.
∠
CB
A
=
2∠
QBP
.
Prove that
∠
A
D
C
=
2
∠
P
D
Q
.
\angle ADC = 2 \angle PDQ.
∠
A
D
C
=
2∠
P
D
Q
.
geometry
angle
circumscribed
quadrilateral