Paragraph for Question Let \( A B C \) be a triangle inscribed in a circle and let \( l_{a}=\fra...

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Paragraph for Question
Let \( A B C \) be a triangle inscribed in a circle and let \( l_{a}=\frac{m_{a}}{M_{a}} ; l_{b}=\frac{m_{b}}{M_{b}} ; l_{c}=\frac{m_{c}}{M_{c}} \) where \( m_{a}, m_{b}, m_{c} \) are the lengths of the angle bisectors of angles \( A, B \) and \( C \) respectively, internal to the triangle and \( M_{a}, M_{b} \) and \( M_{c} \) are the lengths of these internal angle bisectors extended until they meet the circumcircle.
\( l_{a} \) equals :
(a) \( \frac{\sin A}{\sin \left(B+\frac{A}{2}\right)} \)
(b) \( \frac{\sin B \sin C}{\sin ^{2}\left(\frac{B+C}{2}\right)} \)
(c) \( \frac{\sin B \sin C}{\sin ^{2}\left(B+\frac{A}{2}\right)} \)
(d) \( \frac{\sin B+\sin C}{\sin ^{2}\left(B+\frac{A}{2}\right)} \)
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