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All-Russian Olympiad Regional Round
1997 All-Russian Olympiad Regional Round
10.7
10.7
Part of
1997 All-Russian Olympiad Regional Round
Problems
(1)
BD tangent to (O_1O_2A), AB=BC - All-Russian MO 1997 Regional (R4) 10.7
Source:
9/24/2024
Points
O
1
O_1
O
1
and
O
2
O_2
O
2
are the centers of the circumscribed and inscribed circles of an isosceles triangle
A
B
C
ABC
A
BC
(
A
B
=
B
C
AB = BC
A
B
=
BC
). The circumcircles of triangles
A
B
C
ABC
A
BC
and
O
1
O
2
A
O_1O_2A
O
1
O
2
A
intersect at points
A
A
A
and
D
D
D
. Prove that line
B
D
BD
B
D
is tangent to the circumcircle of the triangle
O
1
O
2
A
O_1O_2A
O
1
O
2
A
.
geometry
tangent
isosceles