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Kyiv City MO
Kyiv City MO - geometry
Kyiv City MO Juniors 2003+ geometry
2008.9.5
<BFL=?AF=LC<1/2AC, AB^2+BC^2=AL^2+LC^2 (Kyiv City Olympiad 2008 9.5)
<BFL=?AF=LC<1/2AC, AB^2+BC^2=AL^2+LC^2 (Kyiv City Olympiad 2008 9.5)
Source:
June 30, 2020
geometry
angles
Problem Statement
In the triangle
A
B
C
ABC
A
BC
on the side
A
C
AC
A
C
the points
F
F
F
and
L
L
L
are selected so that
A
F
=
L
C
<
1
2
A
C
AF = LC <\frac{1}{2} AC
A
F
=
L
C
<
2
1
A
C
. Find the angle
∠
F
B
L
\angle FBL
∠
FB
L
if
A
B
2
+
B
C
2
=
A
L
2
+
L
C
2
A {{B} ^ {2}} + B {{C} ^ {2}} = A {{L} ^ {2}} + L {{C } ^ {2}}
A
B
2
+
B
C
2
=
A
L
2
+
L
C
2
(Zhidkov Sergey)
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