To find the distance of the chord from the center of the circle, we can use the relationship between the radius, the distance from the center to the chord, and half the length of the chord.
First, let’s denote:
- Radius of the circle (r) = 10 cm
- Length of the chord (L) = 16 cm
Now, we can find half of the length of the chord:
Half of chord length = L/2 = 16 cm / 2 = 8 cm
Next, we denote the distance from the center of the circle to the chord as ‘d’. Using the Pythagorean theorem in the right triangle formed by the radius, the half chord, and the distance ‘d’, we have:
Substituting the known values:
(10 cm)2 = d2 + (8 cm)2
100 cm2 = d2 + 64 cm2
Now, solving for d2:
d2 = 100 cm2 – 64 cm2
d2 = 36 cm2
Now we find the value of ‘d’ by taking the square root:
d = √(36 cm2) = 6 cm
Thus, the distance of the chord from the center of the circle is 6 cm.