Question

in the adjoining figure ad is the bisector of angle BAC if a b is equals to 10 cm AC is equals to 6 CM BC is equals to 12 cm find BD

Answer 1

In a triangle ABC, AD is the bisector of angle BAC, if AB=6cm, AC=5cm and BD=3, then DC=?



Here, we can see that ∠BAC∠BAC is bisected by AD where AD touches BC at D. BC=BD+DCBC=BD+DCwhere, BC=3cmBC=3cm. We also have the values of adjacent sides AB=6cmAB=6cmand AC=5cmAC=5cm.

These satisfy the requirements of angle bisector theorem. Then, by the theorem, we have:

ABBD=ACDCABBD=ACDC

⇒DC=AC∗BDAB=5∗36=2.5cm⇒DC=AC∗BDAB=5∗36=2.5cm

Happy math!!

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