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Question

In a ABC, AD is the bisector or A.


(i) If AB = 6.4 cm, AC = 8 cm and BD = 5.6 cm, find DC.
(ii) If AB = 10 cm, AC = 14 cm and BC = 6 cm, find BD and DC.
(iii) If AB = 5.6 cm, BD = 3.8 cm and BC = 6 cm, find AC.
(iv) If AB = 5.6 cm, AC = 4 cm and DC = 3 cm, find BC.

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Solution

(i)
It is given that AD bisects A.Applying angle-bisector theorem in ABC, we get:BDDC=ABAC5.6DC=6.48DC = 8×5.66.4 = 7 cm


(ii)
It is given that AD bisects A.Applying angle-bisector theorem in ABC, we get:

BDDC =ABACLet BD be x cm.Therefore, DC = (6-x) cmx6-x = 101414x = 60-10x24x = 60x = 2.5 cmThus, BD = 2.5 cmDC = 6-2.5 = 3.5 cm

(iii)
It is given that AD bisects A.Applying angle-bisector theorem in ABC, we get:

BDDC=ABACBD = 3.2 cm, BC = 6 cmTherefore, DC = 6-3.2 = 2.8 cm3.22.8=5.6AC

AC = 5.6×2.83.2=4.9 cm


(iv)
It is given that AD bisects A.Applying angle-bisector theorem in ABC, we get:

BDDC = ABACBD3 = 5.64BD = 5.6×34BD = 4.2 cm

Hence, BC = 3 + 4.2 = 7.2 cm

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