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Let ABC be a triangle inscribed in a cir...

Let ABC be a triangle inscribed in a circle and let `l_(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 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.
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 equal to :

A

`(1)/(8)`

B

`(1)/(64)`

C

`(27)/(64)`

D

`(27)/(32)`

Text Solution

Verified by Experts

The correct Answer is:
C
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