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You are here: Home / GRE Quant / Geometry / More Than 1 Answer: Circles and Chords

More Than 1 Answer: Circles and Chords

September 7, 2012 By K S Baskar 3 Comments

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

Indicate ALL possible distances

a) 1
b) 7
c) 4
d) 28
e) 2
f) 14

Solution: (C), (D)

Explanation

The two parallel chords can either both be on one side of the centre or on either sides of the centre of the circle.

Case i:

The two chords are AB and CD. OE and OF are perpendiculars to the two chords from O, the centre of the circle. Hence, CF = FD and AE = EB. OD = OB = 20 = radius of the circle. EF is the distance between the two chords.

OE2 + EB2 = OB2
OE = 12

OF2 + FD2 = OD2
OF = 16

EF = OF – OE = 4

Case ii:

Here again,
OE2 + EB2 = OB2
OE = 12
OF2+ FD2 = OD2
OF = 16
But EF = OE + OF = 28

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Filed Under: Geometry Tagged With: More than one answer correct

Reader Interactions

Comments

  1. Agneesh Bose says

    August 30, 2015 at 12:13 pm

    Very good explanation. Thanks

    Reply
  2. ANSHUL GERA says

    September 10, 2015 at 4:24 am

    nice work

    Reply
  3. Unknown says

    November 28, 2015 at 9:52 am

    good explanation

    Reply

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