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SSC CPO 2019 PYQ — Question 124

SSC CPO Tier I - 12th March 2019 - Shift 1 • Quantitative Aptitude • Q124

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In ΔABC, ∠C = 90º and D is a point on CB such that AD is the bisector of angle A. If AC = 5 cm and BC = 12 cm, then what is the length of AD?

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Correct answer: C

Explanation

The correct answer is Option 3 i.e (5√13)/3

AB = (AC2 + BC2)½ = (25 + 144)½ = 13

So,

CosA = AC/AB = 5/13

⇒ 2 cos2(A/2) - 1 = 5/13

⇒ 2cos2(A/2) = 18/13

⇒ cos2(A/2) = 9/13

⇒ cos(A/2) = 3/√13

From the figure:

cos(A/2) = AC/AD = 5/AD

⇒ AD = 5/cos (A/2) =  (5√13)/3