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Sharygin Geometry Olympiad
2022 Sharygin Geometry Olympiad
18
18
Part of
2022 Sharygin Geometry Olympiad
Problems
(1)
Reflection about diagonal in harmonic quad
Source: Sharygin 2022
3/4/2022
The products of the opposite sidelengths of a cyclic quadrilateral
A
B
C
D
ABCD
A
BC
D
are equal. Let
B
′
B'
B
′
be the reflection of
B
B
B
about
A
C
AC
A
C
. Prove that the circle passing through
A
,
B
′
,
D
A,B', D
A
,
B
′
,
D
touches
A
C
AC
A
C
geometry
geometric transformation
reflection