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Germany Contests
German National Olympiad
2019 German National Olympiad
2
2
Part of
2019 German National Olympiad
Problems
(1)
Geometry with three circles and angular bisectors
Source: Germany 2019, Problem 2
6/20/2019
Let
a
a
a
and
b
b
b
be two circles, intersecting in two distinct points
Y
Y
Y
and
Z
Z
Z
. A circle
k
k
k
touches the circles
a
a
a
and
b
b
b
externally in the points
A
A
A
and
B
B
B
. Show that the angular bisectors of the angles
∠
Z
A
Y
\angle ZAY
∠
Z
A
Y
and
∠
Y
B
Z
\angle YBZ
∠
Y
BZ
intersect on the line
Y
Z
YZ
Y
Z
.
geometry