A chord distance 2 cm from the centre of a circle is 8m long. Calculate the length of a chord of the same circle which is 6cm distance from the centre.
The semi-chord has length 400cm, and so forms a right triangle with hypotenuse √160004 cm, which is the radius of the circle.
So, a chord 6 cm from the center will be 2√(160004-36) = 2√159968 = 8√9998
I suspect a typo somewhere ...
To calculate the length of a chord of a circle, we can use the following formula:
\[ \text{Chord Length} = 2 \times \text{Radius} \times \sin(\theta / 2) \]
In this case, we have a chord that is 2 cm from the center of the circle and has a length of 8 m. We want to find the length of another chord that is 6 cm from the center.
First, we need to convert all distances to the same units. Since the chord length is given in meters, we need to convert the distance from the center to meters as well.
Given that the chord length is 8 m, and the distance from the center is 2 cm, we can convert the distance from cm to m:
\[ \text{Distance from center} = 2 \, \text{cm} \times \frac{1}{100} = 0.02 \, \text{m} \]
Now, we can use the formula to calculate the radius of the circle:
\[ \text{Chord Length} = 2 \times \text{Radius} \times \sin(\theta / 2) \]
Substituting the given values:
\[ 8 \, \text{m} = 2 \times \text{Radius} \times \sin(\theta / 2) \]
We can simplify the equation by dividing both sides by 2:
\[ 4 \, \text{m} = \text{Radius} \times \sin(\theta / 2) \]
To find the value of \( \sin(\theta / 2) \), we can use the fact that the distance from the center divided by the radius is equal to \( \sin(\theta / 2) \):
\[ \sin(\theta / 2) = \frac{\text{Distance from center}}{\text{Radius}} \]
Substituting the value of the distance from the center (0.02 m) and rearranging the equation to solve for the radius:
\[ \frac{\text{Distance from center}}{\sin(\theta / 2)} = \text{Radius} \]
\[ \text{Radius} = \frac{0.02 \, \text{m}}{\sin(\theta / 2)} \]
Now, we have the value of the radius of the circle. To find the length of the chord that is 6 cm from the center, we can use the same formula:
\[ \text{Chord Length} = 2 \times \text{Radius} \times \sin(\theta / 2) \]
Substituting the value of the radius we just calculated (0.02 m) and the new distance from the center (6 cm):
\[ \text{Chord Length} = 2 \times 0.02 \, \text{m} \times \sin(\theta / 2) \]
We can simplify and calculate the value of the chord length:
\[ \text{Chord Length} = 0.04 \, \text{m} \times \sin(\theta / 2) \]
To find the exact length of the chord, we need to know the measure of the central angle \( \theta \). Without this information, we cannot calculate the length of the chord precisely.