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CAT 2005 — QA Question 9

Basics of CirclesEasy

What is the distance in cm between two parallel chords of lengths 32 cm and 24 cm in a circle of radius 20 cm?

Answer & solution

Correct answer: 4 or 28

  • A

    1 or 7

  • B

    2 or 14

  • C

    3 or 21

  • 4 or 28

Solution

The two chords AB and CD can be on the same side or the opposite sides of the centre O.

Let M and N be the midpoints of AB and CD.
∴ MN is the distance between the two chords.

MB = 12 cm and ND = 16 cm

OM and ON are perpendicular to AB and CD respectively.

ON2 = OD2 - ND2 (By Pythagoras theorem)
⇒ ON2 = 202 – 162 ​​​​​​​
⇒ ON = 12 cm

Similarly,OM2 = OB2 - MB2 
⇒ OM = 16 cm 

Case 1: AB and BC are on the same side of the centre.
MN = OM – ON = 4 cm

Case 2: AB and BC are on opposite sides of the centre.
MN = OM + ON = 28 cm

Hence, option (d).

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CAT 2005 QA Q9: What is the distance in cm between two parallel chords of lengths 32 cm and 24 cm in a circle of radius 20 cm? — Solution | TheCATExam