In a circle, the chord is the line that connects two points within the circle. Calculating the chord is an important skill to learn, especially since the chord is used in plenty of trigonometric and mathematical problems. It is possible for you to calculate the length of the chord using only the angle between the endpoints connecting the chord in relation to the center of the circle, and the length of the radius. Here’s how you can do it.
Define the terms. To be able to efficiently calculate the chord length for a circle, you should be able to define all of the terms that you will use. Keep in mind that you will transform the points and measurements in the circle into a formula, which means that you should know exactly where your terms are located in the actual circle. Imagine a circle, with two points somewhere around the edge. These two points can be called A and B, and are what constitutes your chord. You should also identify the other parts of the circle that will help you compute for the chord length, such as the radius. The radius is the distance from the center to any point on the circle. The chord length is the measurement between points A and B.
Using the radius and central angle. To compute for the chord length using the radius, you need to get the measurements for the radius as well as the central angle. The central angle is the angle formed between points A and B from the chord, intersecting at the center of the circle. Once you have these measurements, you will need to compute using this formula: 2rsin(c/2). This formula means that the radius will be multiplied twice and then multiplied with the sin function. This will then be multiplied by the result of the central angle divided by two. This means that if you have an angle of 60 degrees and if the length of the radius on your circle is 3, the chord length is equal to three.
Other calculations. You can also compute for the length of the chord using the radius and the chord’s distance from the center of the circle. The distance of the chord from the center is the line from the center of the circle to the midpoint of the chord as it passes from point A to B. once you have these measurements, you will need to use the formula: 2(r^2-d^2)^(1/2). To simplify the equation, begin inside the parenthesis first. Solve the exponents for the radius and the distance first, and then subtract the two. This will then be multiplied by two and raised to ½ power. This means that if the distance is equal to three and the radius is five, you have a chord length of eight.
The next time you face a science project or mathematical problem that requires you to solve for the length of the chord in a circle, use these formulas to compute for the chord length using only the radius and central angle or distance from the chord to the radius.