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Bulgarian Spring Mathematical Competition
2023 Bulgarian Spring Mathematical Competition
11.2
11.2
Part of
2023 Bulgarian Spring Mathematical Competition
Problems
(1)
weird ratio in a cyclic quad
Source: Bulgarian Spring Tournament 2023 11.2
3/25/2023
Given is a cyclic quadrilateral
A
B
C
D
ABCD
A
BC
D
and a point
E
E
E
lies on the segment
D
A
DA
D
A
such that
2
∠
E
B
D
=
∠
A
B
C
2\angle EBD = \angle ABC
2∠
EB
D
=
∠
A
BC
. Prove that
D
E
=
A
C
.
B
D
A
B
+
B
C
DE= \frac {AC.BD}{AB+BC}
D
E
=
A
B
+
BC
A
C
.
B
D
.
geometry