More Than 1 Answer: Circles and Chords

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)

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

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

Here again,

OE² + EB² = OB²

OE = 12

OF²+ FD² = OD²

OF = 16

But EF = OE + OF = 28