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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. `l_(a)` equals :

A

`(sinA)/(sin(B+(A)/(2)))`

B

`(sinBsinC)/(sin^(2)((B+C)/(2)))`

C

`(sinBsinC)/(sin^(2)(B+(A)/(2)))`

D

`(sinB+sinC)/(sin^(2)(B+(A)/(2)))`

Text Solution

Verified by Experts

The correct Answer is:
C
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