One chord of a circle is given as 20 5 cm Then the radius r of the circle must be ........

Quantitative Aptitude (CGL) Geometry

One chord of a circle is given as 20.5 cm. Then the radius (r) of the circle must be:

This questions was previously asked in

SSC CGL Tier II Paper 1 (26.10.2023)

r = 10cm

r < 10.25

r > 10.25

r ≥ 10.25

- For any chord of a circle, the maximum possible length occurs when the chord is the diameter.

- The given chord length is 20.5 cm.

- So, the minimum radius possible is half the chord length: \( r = 20.5 / 2 = 10.25 \) cm.

- The radius cannot be less than 10.25 cm, otherwise, a 20.5 cm chord cannot fit in the circle.

- Option 1: r = 10 cm — Not possible, as 2r = 20 cm < 20.5cm.

- Option 2: r < 10.25 cm — Not possible for the same reason.

- Option 3: r > 10.25 cm — Possible, but does not include r = 10.25 cm.

- Option 4: r = 10.25 cm — Correct, as the minimum radius to allow the chord is 10.25 cm, and greater is possible as well.

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