1.

CF is the internal bisector of angle C of angle ABC, then CF is equal to

Answer»

`(2AB)/(a + B) cos.(C)/(2)`
`(a +b)/(2ab) cos.(C)/(2)`
`(b sin A)/(sin(B + (C)/(2)))`
none of these

Solution :
`DELTA = Delta_(1) + Delta_(2)`
`rArr (1)/(2) ab sin C = (1)/(2) b (CF) sin .(C)/(2) + (1)/(2) a (CF) sin.(C)/(2)`
or `CF = (ab sin C)/((a + b) sin.(C)/(2)) = (2ab cos.(C)/(2))/(a+b)`
Again in `DeltaCFB`, by the sine rule, we have
`(CF)/(sin B) = (a)/(sin (pi -theta)) = (a)/(sin theta) = (a)/(sin (B+(C)/(2))) ""( :' theta + B + (C)/(2) = pi)`
or `CF = (a sin B)/(sin (B +(C)/(2))) = (b sin A)/(sin (B +(C)/(2)))` [by sine rule]


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