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SSC CGL 2019 PYQ — Question 54

SSC CGL - 7th June 2019 - Shift 1 • Quantitative Aptitude • Q54

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In ΔABC, AD bisects ∠A and intersects BC at D. If BC = a, AC = b and AB = c, then BD = ?

Show answer & explanation

Correct answer: C

Explanation

The correct answer is option 3 i.e. ac/(b + c)

Concept

Understanding

Application

Bisector of an angle X divides the opposite side in the ratio of respective sides containing that angle.

Given:

BC = a, AC = b and AB = c

Bisector of ∠A divides BC in the ratio of respective sides containing angle A.

Hence,

BD/CD = AB/AC = c/b

BD + CD = a (given)

⇒ BD (1 + CD/BD) = a

⇒ BD (1 + b/c) = a

⇒ BD = ac/(b + c)