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SSC CPO 2019 PYQ — Question 144

SSC CPO Tier I - 12th December 2019 - Shift 1 • Quantitative Aptitude • Q144

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In triangle ABC, ∠C = 90°, and D is the point on CB such that AD is the bisector of ∠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 cm

Application

Given that In ∆ABC, ∠C = 90o and D is a point on CB such that AD is the bisector of ∠A

Figure for the explanation of question 144

In right-angled ∆ABC

Using Pythagoras Theorem

(AB)2 = (AC)2 + (BC)2

(AB)2 = 52 + 122 = 169

AB = √169 = 13

Now using the Angle bisector theorem, we can write

(BD/BA) = (CD/CA)

(BD/CD) = (BA/CA) = 13/5

Hence BD : DC = 13 : 5 & BC = 12 cm

= DC = 5/18 × 12 = 10/3 cm

In right-angled triangle ACD

Using Pythagoras Theorem

(AD)2 = (CD)2 + (AC)2

(AD)2 = (10/3)2 + (5)2 = 325/9

AD = √(5 × 5 × 13)/(3 × 3) = 5√13/3 cm