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SSC CGL 2025 PYQ — Question 55

SSC CGL - 16 Sep 2025 - Shift 1 • Quantitative Aptitude • Q55

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A right triangle ABC is inscribed in a circle with a diameter of 10 cm. An altitude BD is drawn from the vertex B to the hypotenuse AC. If the length of the leg AB is 6 cm, what is the length of the segment AD?

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 3.6 cm.

Diameter of circle = 10 cm

Hypotenuse AC = 10

Given, AB = 6

BC2 = AC2 − AB2

⇒ BC2 = 10² − 6²

⇒ BC2 = 100 − 36 = 64

⇒ BC = 8

In a right triangle:

AD = AB2ACAB^2 \over AC

AD = 62106^2 \over10 = 361036 \over 10 = 3.6 cm