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Problems
Mathematics
Mathematics
Problem
The base
A
B
AB
A
B
of a triangle is fixed and its vertex
C
C
C
moves such that
sin
A
=
k
sin
B
\sin A = k \sin B
sin
A
=
k
sin
B
(
k
≠
1
k \neq 1
k
=
1
). Show that the locus of
C
C
C
is a circle whose centre lies on the line
A
B
AB
A
B
and whose radius is equal to
a
k
(
1
−
k
2
)
\frac{ak}{(1-k^2)}
(
1
−
k
2
)
ak
,
a
a
a
being the length of the base
A
B
AB
A
B
.
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