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CF is the internal bisector of angle C of angle ABC, then CF is equal to |
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Answer» `(2AB)/(a + B) cos.(C)/(2)` `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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