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Old Kyiv MO Geometry
Kyiv City MO Seniors 2003+ geometry
2014.11.4.1.
2014.11.4.1.
Part of
Kyiv City MO Seniors 2003+ geometry
Problems
(1)
circles intersection is midpoint of chord, 3 circles (2014 Kyiv City MO 11.4.1)
Source:
8/6/2020
Construct for the triangle
A
B
C
ABC
A
BC
a circle
S
S
S
passing through the point
B
B
B
and touching the line
C
A
CA
C
A
at the point
A
A
A
, a circle
T
T
T
passing through the point
C
C
C
and touches the line
B
A
BA
B
A
at the point
A
A
A
. The second intersection point of the circles
S
S
S
and
T
T
T
is denoted by
D
D
D
. The intersection point of the line
A
D
AD
A
D
and the circumscribed circle
Δ
A
B
C
\Delta ABC
Δ
A
BC
is denoted by
E
E
E
. Prove that
D
D
D
is the midpoint of the segment
A
E
AE
A
E
.
geometry
circles
midoint