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SSC CGL 2024 PYQ — Question 75

SSC CGL - 26 Sep 2024 - Shift 1 • Quantitative Aptitude • Q75

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From a point A, which is at a distance of 17 cm from the centre C of a circle with radius 8 cm, the pair of tangents AB and AD to the circle are drawn. The area of the quadrilateral ABCD is _____ cm2.

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 120.

CB = CD = 8 cm (radius) and CA = 17 cm

The tangent at any point on a circle is perpendicular to the radius through the point of contact.

So, CB is perpendicular to AB, and CD is perpendicular to AD.

Here, triangles CAB and CAD are right-angled triangles.

In triangle CAB, AB=CA2−CB2=172−82=225=15AB=\sqrt{CA^2-CB^2}=\sqrt{17^2-8^2}=\sqrt{225}= 15 cm

AB = AD = 15 cm

Area of triangle CAB = Area of triangle CAD = (1/2) × 8 × 15 = 60 cm2

Area(ABCD) = Area(△CAB) + Area(△CAD) = 60 + 60 = 120 cm2

Therefore, the area of the quadrilateral ABCD is 120 cm2.