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SSC CGL 2016 PYQ — Question 81

SSC CGL Tier II Quant - 01/12/2016 • Quantitative Aptitude • Q81

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ΔABC is an isosceles triangle inscribed in a circle. If AB = AC = 12√5 cm and BC = 24 cm then find the radius of the circle.

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 15 cm.

Figure for the explanation of question 81

AD is perpendicular to BC:

Given, BC = 24 cm

BD = DC = 12 cm

OC = OA = Circumradius = r cm

AD = √[AB2 - BD2]

⇒ AD = √[(12√5)2 - (12)2]

⇒ AD = √[144 × 5 - 144]

⇒ AD = √[144 × 4] = 24 cm.

In triangle OCD,

OD = (24 - r) cm.

OC2 = OD2 + CD2

⇒ r2 = (24 – r)2 + 122

⇒ r2 = 576 – 48r + r2 + 144

⇒ 48r = 720

⇒ r = 720/48 = 15 cm