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
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