Let ABC be a triangle inscribed in a circle and letl_(a)=(m_(a))/(M_(a)), l_(b)=(m_(b))/(M_(b)), l_(c )=(m_(c ))/(M_(c )) where m_(a), m_(b), m_(c ) are the lengthsof 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 internalangle bisectors extended until they meet the circumcircle. Q.The maximum value of the product(l_(a)l_(b)l_(c))xxcos^(2)((B-C)/(2)) xx cos^(2)(C-A)/(2)) xx cos^(2)((A-B)/(2)) is equalto :

Let ABC be a triangle inscribed in a circle and letl_(a)=(m_(a))/(M_(a

1.	Let ABC be a triangle inscribed in a circle and letl_(a)=(m_(a))/(M_(a)), l_(b)=(m_(b))/(M_(b)), l_(c )=(m_(c ))/(M_(c )) where m_(a), m_(b), m_(c ) are the lengthsof 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 internalangle bisectors extended until they meet the circumcircle. Q.The maximum value of the product(l_(a)l_(b)l_(c))xxcos^(2)((B-C)/(2)) xx cos^(2)(C-A)/(2)) xx cos^(2)((A-B)/(2)) is equalto :
Answer» `(1)/(8)` `(1)/(64)` `(27)/(64)` `(27)/(32)` ANSWER :C

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