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SSC CGL 2024 PYQ — Question 59

SSC CGL - 25 Sep 2024 - Shift 1 • Quantitative Aptitude • Q59

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The centres of two circles are 36 cm apart. If the radii of these two circles are 15 cm and 9 cm, respectively, then what is the sum of the lengths (in cm) of a direct common tangent and a transverse common tangent of these two circles?

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 6√5(√7 + 2).

Here, OA = 15 cm and PB = PC = 9 cm

Distance between two centers (OP) = 36 cm

The length of the direct common tangent =OP2−(OA−PB)2=\sqrt{OP^2-(OA-PB)^2}

=362−(15−9)2=\sqrt{36^2-(15-9)^2}

=362−62=\sqrt{36^2-6^2}

= √1260 = 6√35 cm

The length of the transverse common tangent =OP2−(OA+PB)2=\sqrt{OP^2-(OA+PB)^2}

=362−(15+9)2=\sqrt{36^2-(15+9)^2}

=362−242=\sqrt{36^2-24^2}

= √720

= 12√5 cm

Now, 6√35 + 12√5 = 6√5(√7 + 2) cm

Therefore, the required value is 6√5(√7 + 2) cm.