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Bulgaria Contests
Bulgarian Spring Mathematical Competition
2023 Bulgarian Spring Mathematical Competition
10.2
10.2
Part of
2023 Bulgarian Spring Mathematical Competition
Problems
(1)
Easy isosceles triangle geo
Source: Bulgarian Spring Tournament 2023 10.2
3/25/2023
An isosceles
△
A
B
C
\triangle ABC
△
A
BC
has
∠
B
A
C
=
∠
A
B
C
=
7
2
o
\angle BAC =\angle ABC =72^{o}
∠
B
A
C
=
∠
A
BC
=
7
2
o
. The angle bisector
A
L
AL
A
L
meets the line through
C
C
C
parallel to
A
B
AB
A
B
at
D
D
D
.
a
)
a)
a
)
Prove that the circumcenter of
△
A
D
C
\triangle ADC
△
A
D
C
lies on
B
D
BD
B
D
.
b
)
b)
b
)
Prove that
B
E
B
L
\frac {BE} {BL}
B
L
BE
is irrational.
geometry