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How do you find the chord length when radius is given?
To find the chord length when the radius is given, you can use the formula: ( L = 2 \times r \times \sin\left(\frac{\theta}{2}\right) ), where ( L ) is the chord length, ( r ) is the radius, and ( \theta ) is the central angle in radians subtended by the chord at the center of the circle. If the angle is not provided, you can also use the relationship involving the distance from the center to the chord (perpendicular distance) to find the chord length.
What is the length drawn from one side to another in a circle?
The length drawn from one side of a circle to another is called a chord. A chord connects two points on the circumference of the circle and is shorter than or equal to the diameter, which is the longest chord in the circle. The distance from the center of the circle to the chord is known as the chord's perpendicular distance.
How do you find the radius of a circle if you know the length of a chord and the shortest distance from the center of the chord to the circle?
Imagine if you will a circle with a chord drawn through it and a line running from the center of that chord to the center of the circle. That line is necessarily perpendicular to the chord. This means you have a right triangle whose hypotenuse is the radius of the circle. The radius is thus given by: r = sqrt{(1/2 chord length)^2 + (length of perpendicular line)^2} The actual formula to find the radius is as follows: r= C squared/8a + a/2, where C is the chord length, and a is the distance from center point of the chord to the circle , and a and C form an angle of 90 degrees. the entire formula before simplification is r = sqrt {(1/2 C)^2 + (r-a)^2}
In a circle whose diameter is 20in and a chord is 6in from the center what is the length of the chord?
the chord is 4in long
Can a chord be many different lengths?
Yes, a chord can vary in length based on its position within a circle. The length of a chord is determined by the distance between its endpoints, which can change depending on how far the endpoints are from the center of the circle. Therefore, a chord can indeed have many different lengths, ranging from zero (when it collapses to a point) to the diameter of the circle (the longest possible chord).
How do you find the chord length when radius is given?
To find the chord length when the radius is given, you can use the formula: ( L = 2 \times r \times \sin\left(\frac{\theta}{2}\right) ), where ( L ) is the chord length, ( r ) is the radius, and ( \theta ) is the central angle in radians subtended by the chord at the center of the circle. If the angle is not provided, you can also use the relationship involving the distance from the center to the chord (perpendicular distance) to find the chord length.
What is the length drawn from one side to another in a circle?
The length drawn from one side of a circle to another is called a chord. A chord connects two points on the circumference of the circle and is shorter than or equal to the diameter, which is the longest chord in the circle. The distance from the center of the circle to the chord is known as the chord's perpendicular distance.
How do you find the radius of a circle if you know the length of a chord and the shortest distance from the center of the chord to the circle?
Imagine if you will a circle with a chord drawn through it and a line running from the center of that chord to the center of the circle. That line is necessarily perpendicular to the chord. This means you have a right triangle whose hypotenuse is the radius of the circle. The radius is thus given by: r = sqrt{(1/2 chord length)^2 + (length of perpendicular line)^2} The actual formula to find the radius is as follows: r= C squared/8a + a/2, where C is the chord length, and a is the distance from center point of the chord to the circle , and a and C form an angle of 90 degrees. the entire formula before simplification is r = sqrt {(1/2 C)^2 + (r-a)^2}
In a circle whose diameter is 20in and a chord is 6in from the center what is the length of the chord?
the chord is 4in long
A chord of a circle has length 4.2 cm and is 8 cm from the center of the circle what is the radius of the circle?
To find the radius of the circle, we can use the Pythagorean theorem. The chord divides the circle into two equal parts, each forming a right triangle with the radius. The radius, the distance from the center to the chord, and half the length of the chord form a right triangle. Using the Pythagorean theorem, we have (radius)^2 = (distance from center)^2 + (1/2 * chord length)^2. Substituting in the given values, we get (radius)^2 = 8^2 - (1/2 * 4.2)^2. Solving for the radius gives us a radius of approximately 7.48 cm.
Can a chord be many different lengths?
Yes, a chord can vary in length based on its position within a circle. The length of a chord is determined by the distance between its endpoints, which can change depending on how far the endpoints are from the center of the circle. Therefore, a chord can indeed have many different lengths, ranging from zero (when it collapses to a point) to the diameter of the circle (the longest possible chord).
What is the relation between radius and chord length of circle?
This requires trigonometry If theta is the angle from the center of the circle to the edges of the chord, then chord length = 2Rsin (theta/2)
How do you find the radius diameter and chord?
To find the radius of a circle, measure the distance from the center to any point on the circle's edge. The diameter is twice the radius, so you can calculate it by multiplying the radius by two. A chord is a straight line segment whose endpoints lie on the circle; you can measure its length directly with a ruler or use the formula for a chord length if the radius and the angle subtended at the center are known.
Why is the diameter the longest chord?
A chord is a straight line from one point on a circle's circumference to another. Because the largest straight line distance in a circle is the diameter and the diameter is also a chord, the diameter is the longest chord. Join the endpoints of a given chord to the center of the circle to form an isosceles triangle. The triangle inequality then tells that the length of the chord is less than two radii of the circle, i.e., less than the diameter. See related links.
Is a chord always equal to the length of the diameter?
No; actually, the diameter is a chord that goes through the center of a circle.
What is a line segment that has both endpoints on the circle?
This is referred to as a chord. If the chord passes through the center of the circle, it represents the diameteror width of the circle.For a circle, the length of the diameter is the longest possible length of a chord.
What is a group of related tones with common center called?
A chord
