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SSC CPO 2024 PYQ — Question 145

SSC CPO - 29 June 2024 - Shift 1 • Quantitative Aptitude • Q145

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The distance between the centres of the two circles, with radii 3 cm and 2 cm, respectively, is 13 cm. The length (in cm) of a transverse common tangent is:

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 12 cm.

Given that, distance between centres of the circles, d = 13 cm

Radius of first circle, r1 = 2 cm

Radius of second circle, r2 = 3cm

Transverse common tangent, L = d2−(r2+r1)2\sqrt{d^2 -(r_2 + r_1)^2}

According to the given question,

L = d2−(r2+r1)2\sqrt{d^2 -(r_2 + r_1)^2}

⇒ L = 132−(3+2)2\sqrt{13^2 -(3 + 2)^2}

⇒ L = 132−52\sqrt{13^2 - 5^2}

⇒ L = 169−25\sqrt{169 - 25}

⇒ L = 12 cm

Hence the length of the transverse common tangent is 12 cm.