showing a circle with centre 0. 0M and 0N meet the chords PR and RS perpendicularly at M and N respectively Given that PR=12cm and RS=16cm find the radius

To find the radius of the circle, we can make use of the fact that the perpendicular from the center of a circle to a chord bisects the chord.

Let's label the center of the circle as O. Since M and N are the points where the chords PR and RS are perpendicular to the diameter ON and OM respectively, we know that OM = MN = radius (let's call it r).

We can draw the diagram, recalling that the chords are perpendicular to the diameter as given.

```
P
\
\
O---------R
/ \
/ \
M N
/
/
S

```

We know that PR = 12 cm and RS = 16 cm. Since the diameter ON = 2r, we can find the value of MN using the Pythagorean theorem.

Applying the theorem in triangle PMO:
(MN)^2 + (OM)^2 = (PR/2)^2

Substituting the known values:
r^2 + r^2 = (12/2)^2

Simplifying the expression:
2r^2 = 6^2
2r^2 = 36

Dividing both sides by 2:
r^2 = 18

Taking the square root of both sides:
r = √18

Simplifying:
r ≈ 4.242 cm

Therefore, the radius of the circle is approximately 4.242 cm.