Two parallel chords are drawn in a circle of diameter 30 cm The length of one chord is 24 cm and the...........

Quantitative Aptitude ( CCS) Geometry

Two parallel chords are drawn in a circle of diameter 30 cm. The length of one chord is 24 cm and the distance between the two chords is 21 cm. The length of the other chord is

9 cm

14 cm

18 cm

27 cm

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Explanation:

Given, one chord AB =24cm
Then, AE = EB = 12 cm
Diameter =30cm
⇒ radius, AO = OC = 15 cm
From ΔAOE, By pythagoras theorem
OE = √(OA² – AE²)
= √(15² – 12²)= √81= 9 cm
Distance between two chords, EF = 21 cm (given)
∴ OF = EF – OE = 21 – 9 = 12 cm
From ΔCOF, By pythagoras theorem
CF = OC² – OF²
= √(15²– 12²)= 81= 9 cm
∴ CD = 2 × 9 = 18 cm