In a circle with center O and radius 5 cm AB and CD are two parallel chords of lengths 6 cm and x cm...........

Quantitative Aptitude (CGL) Geometry

In a circle with center O and radius 5 cm, AB and CD are two parallel chords of lengths 6 cm and x cm, respectively and the

chords are on the opposite side of the centre O . The distance between the chords is 7 cm. What is the value of x?

This questions was previously asked in

SSC CGL 16th August 2021 Shift-1

- We have a circle with center O and radius 5 cm.

- AB and CD are parallel chords with lengths 6 cm and x cm, respectively.

- The distance between the chords AB and CD is given as 7 cm.

- Using the properties of a circle, we can calculate the distances from the center O to each chord.

- For chord AB (6 cm), the distance from O, denoted as d1, satisfies the equation: \( d1^2 + (6/2)^2 = 5^2 \).

- Solving gives: \( d1 = 4 \).

- The distance from the center O to chord CD, denoted as d2, is \( d2 = d1 + 7 = 4 + 7 = 11 \).

- For chord CD (x cm), use: \( d2^2 + (x/2)^2 = 5^2 \).

- Plugging in \( d2 = 11 \), we find \( x = 8 \).

?? Correct Answer: Option 3, 8

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