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Problems
Contests
National and Regional Contests
Russia Contests
All-Russian Olympiad Regional Round
1995 All-Russian Olympiad Regional Round
10.3
10.3
Part of
1995 All-Russian Olympiad Regional Round
Problems
(1)
tangents meet on median All-Russian MO 1995 Regional (R4) 10.3
Source:
8/26/2024
In an acute-angled triangle
A
B
C
ABC
A
BC
, the circle
S
S
S
with the altitude
B
K
BK
B
K
as the diameter intersects
A
B
AB
A
B
at
E
E
E
and
B
C
BC
BC
at
F
F
F
. Prove that the tangents to
S
S
S
at
E
E
E
and
F
F
F
meet on the median from
B
B
B
.
geometry
Tangents
median