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SSC CGL 2025 PYQ — Question 52

SSC CGL - 19 Sep 2025 - Shift 1 • Quantitative Aptitude • Q52

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A circle is inscribed in a right triangle with legs of length 5 cm and 12 cm. What is the radius of the circle?

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 2 cm.

Hypotenuse =52+122=25+144=169=13=\sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13 cm

Area = (1/2) × Base × Height = (1/2) × 5 × 12 = 30 cm2

Semiperimeter (s) = (5 + 12 + 13)/2 = 30/2 = 15 cm

Inradius = Area/Semiperimeter = 30/15 = 2 cm