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.

OE

^{2}+ EB^{2}= OB^{2}OE = 12

OF

^{2}+ FD^{2}= OD^{2}OF = 16

EF = OF – OE = 4

#### Case ii:

Here again,

OE

^{2}+ EB^{2}= OB^{2}OE = 12

OF

^{2}+ FD^{2}= OD^{2}OF = 16

But EF = OE + OF = 28

Agneesh Bose says

Very good explanation. Thanks

ANSHUL GERA says

nice work

Unknown says

good explanation