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National and Regional Contests
Russia Contests
Sharygin Geometry Olympiad
2022 Sharygin Geometry Olympiad
10.4
10.4
Part of
2022 Sharygin Geometry Olympiad
Problems
(1)
Common internal tangent passes through a midpoint of a diagonal
Source: Sharygin 2022 Finals 10-11.4
8/2/2022
Let
A
B
C
D
ABCD
A
BC
D
be a convex quadrilateral with
∠
B
=
∠
D
\angle B= \angle D
∠
B
=
∠
D
. Prove that the midpoint of
B
D
BD
B
D
lies on the common internal tangent to the incircles of triangles
A
B
C
ABC
A
BC
and
A
C
D
ACD
A
C
D
.
geometry