Multiple choice

In the given questions, two quantities are given, one as ‘Quantity I’ and another as ‘Quantity II’. You have to determine relationship between two quantities and choose the appropriate option: Quantity I: ‘x’ : Area of circle is ‘x’ in which two chords PQ and EF meet at a point S inside a circle. These chords are perpendicular to each other. PS = 12 cm, SQ = 8 cm and FS = 6 cm. Quantity II: ‘y’ : Area of circle is ‘y’ in which two chords are drawn on opposite sides of a diameter. Both chords are parallel to each other. Distance between these chords is 14 cm. Length of one chord is 16 cm while length of another chord is 12 cm.

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or No relation
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A Correct answer
Explanation

Quantity I: Using intersecting chords theorem, PS × SQ = FS × SE. 12 × 8 = 6 × SE, so SE = 16. Radius r = √[(PS + SQ)² + (FS + SE)²]/4 = √[20² + 22²]/4 = √844/4 ≈ 7.27, Area ≈ 166. Quantity II: Distance between chords = 14. Using geometry, if chords are on opposite sides of diameter, the circle radius relates to their lengths. This area is smaller (~125-150 range). Quantity I > Quantity II.

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