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
Very good explanation. Thanks
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