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SSC CGL 2016 PYQ — Question 84

SSC CGL Tier II Quant - 01/12/2016 • Quantitative Aptitude • Q84

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O is the circumcentre of the isosceles Δ ABC. Given that AB = AC = 5 cm and BC = 6 cm. The radius of the circle is:

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Correct answer: D

Explanation

The correct answer is Option 4 i.e. 3.125 cm

Application

Figure for the explanation of question 84

AB = AC = 5 cm. (We have assumed to reach answer)

AD is perpendicular to BC.

BD = DC = 3 cm.

In triangle ADB,

AD = √AB2 - BD2

⇒ AD = √52 - 32

⇒ AD = √25 - 9 = √16 = 4 cm.

Let, OA = OC = r cm.

⇒ OD = (4 – r) cm.

In triangle OCD:

OC2 = OD2 + DC2

⇒ r2 = (4 - r)2 + 32

⇒ r2 = 16 + r2 - 8r + 9

⇒ 8r = 25

⇒ r = 25/8 = 3.125 cm