PQ is a diameter of a circle and PS is a chord. If PQ is 82cm and PS is 80cm, the distance (in cm) of PS from the center of the circle is:

Given:
Diameter PQ=82cm⟹Radius (R)=
2
82
​
=41cm

Chord PS=80cm

Let O be the center of the circle. We want to find the perpendicular distance from O to the chord PS. Let's drop a perpendicular from O to PS and call the intersection point M.

A perpendicular drawn from the center of a circle to a chord bisects the chord:

PM=MS=
2
PS
​
=
2
80
​
=40cm
Now consider the right-angled triangle △OMP (where ∠OMP=90
∘
):

OP
2
=OM
2
+PM
2

Here, OP is the radius (41cm):

41
2
=OM
2
+40
2

1681=OM
2
+1600
OM
2
=1681−1600=81
OM=
81

​
=9cm
Therefore, the distance of the chord from the center is 9cm.