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Old Kyiv MO Geometry
Kyiv City MO Seniors 2003+ geometry
2017.11.5.1
2017.11.5.1
Part of
Kyiv City MO Seniors 2003+ geometry
Problems
(1)
tangent circumcircles at given point wanted (2017 Kyiv City MO 11.5.1)
Source:
9/9/2020
The bisector
A
D
AD
A
D
is drawn in the triangle
A
B
C
ABC
A
BC
. Circle
k
k
k
passes through the vertex
A
A
A
and touches the side
B
C
BC
BC
at point
D
D
D
. Prove that the circle circumscribed around
A
B
C
ABC
A
BC
touches the circle
k
k
k
at point
A
A
A
.
geometry
circumcircle
tangent circles