The radius of a circle is 8centemetre and the length of one of its chords is 12centemetre.find the distance of the chord from the centre.
Did you make a sketch ?
Draw a perpendicular from the centre to the chord and you have a right-angled triangle.
h^2+ 6^2 = 8^2
h^2 = 64-36 = 28
h = √28 cm
To find the distance of the chord from the center of the circle, we can use the property that the distance from the center to the chord is equal to half the length of the chord.
Given that the radius of the circle is 8 centimeters and the length of the chord is 12 centimeters, we can start by drawing a diagram:
```
O
/|\
/ | \
/ | \
/ | \
/ | \
/ | \
/ | \
/ d|d \
/_______|_______\
6cm 6cm
```
In the diagram, we have a circle with center O, radius 8 centimeters, and a chord AB with a length of 12 centimeters. We want to find the distance d from the center O to the chord AB.
Since the distance from the center to the chord is equal to half the length of the chord, we can calculate it as follows:
d = (1/2) * 12 cm
d = 6 cm
Therefore, the distance of the chord from the center is 6 centimeters.