MathDB
Problems
Contests
National and Regional Contests
Russia Contests
Sharygin Geometry Olympiad
2024 Sharygin Geometry Olympiad
8
8
Part of
2024 Sharygin Geometry Olympiad
Problems
(1)
A pair of equal sides, and a pair of equal angles!
Source: Sharygin Correspondence Round 2024 P8
3/6/2024
Let
A
B
C
D
ABCD
A
BC
D
be a quadrilateral
∠
B
=
∠
D
\angle B = \angle D
∠
B
=
∠
D
and
A
D
=
C
D
AD = CD
A
D
=
C
D
. The incircle of triangle
A
B
C
ABC
A
BC
touches the sides
B
C
BC
BC
and
A
B
AB
A
B
at points
E
E
E
and
F
F
F
respectively. Prove that the midpoints of segments
A
C
,
B
D
,
A
E
,
AC, BD, AE,
A
C
,
B
D
,
A
E
,
and
C
F
CF
CF
are concyclic.
geometry
quadrilateral