Question
In a ΔABC, AD is the bisector of ∠A, meeting side BC at D.
If AB = 10 cm, AC =14 cm and BC =6 cm, find BD and DC.
Solution
In ΔABC, AD is the bisector of ∠A
We know that, the internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.
`therefore"BD"/"DC"="AB"/"AC"`
`rArrx/(6-x)=10/14`
⇒ 14x = 10(6 – x)
⇒ 24x = 60
`rArrx=60/24=5/2=2.5 ` cm
Since, DC = 6 – x = 6 – 2.5 = 3.5 cm
Hence, BD = 2.5cm, and DC = 3.5 cm
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Solution In a δAbc, Ad is the Bisector of ∠A, Meeting Side Bc at D. If Ab = Lo Cm, Ac =14 Cm and Bc =6 Cm, Find Bd and Dc. Concept: Angle Bisector.
