Recent questions in Chords

High school geometryAnswered question

Rosemary Chase 2022-11-15

Sum and average length of chords

From a specific point A on a circle's circumference, am drawing various chords. a) what is the sum of length of such chords and b) what is the average length of such chords?

Assuming a radius r, I'm trying to solve a) in the below manner:

One specific chord length $=2r\mathrm{cos}(\mathrm{\Theta})$

To get the sum, I'm integrating over $-\pi /2\text{}to\text{}\pi /2(2r\mathrm{cos}(\mathrm{\Theta})d\mathrm{\Theta})$

But i don't think this is right. Please point me in the correct direction.

From a specific point A on a circle's circumference, am drawing various chords. a) what is the sum of length of such chords and b) what is the average length of such chords?

Assuming a radius r, I'm trying to solve a) in the below manner:

One specific chord length $=2r\mathrm{cos}(\mathrm{\Theta})$

To get the sum, I'm integrating over $-\pi /2\text{}to\text{}\pi /2(2r\mathrm{cos}(\mathrm{\Theta})d\mathrm{\Theta})$

But i don't think this is right. Please point me in the correct direction.

High school geometryAnswered question

Maribel Vang 2022-10-29

Suppose we are given a convex n-gon and all possible pairs of non adjacent vertices are joined to form chords. Let f(n) be the number of pairs of intersecting chords. So $f(4)=1,f(5)=5$. I want to determine f(n) in general.

Some thoughts:

Its not clear to me as to why f(n) is well defined.

$f(n)=f(n-1)+$ something. I want to determine that something.

Is f(n) an upper bound for the crossing number of ${K}_{n}$?

Some thoughts:

Its not clear to me as to why f(n) is well defined.

$f(n)=f(n-1)+$ something. I want to determine that something.

Is f(n) an upper bound for the crossing number of ${K}_{n}$?

High school geometryAnswered question

Mattie Monroe 2022-10-27

Total Number of different playable chords

Suppose that I have a very special Ukulele that contains N frets. I can use atmost 4 fingers to play a chord. I am required to determine the total number of different chords that I can play.

Note: Two chords are different if one of the frets that are pressed in one of the chords is not pressed in another chord.

Suppose that I have a very special Ukulele that contains N frets. I can use atmost 4 fingers to play a chord. I am required to determine the total number of different chords that I can play.

Note: Two chords are different if one of the frets that are pressed in one of the chords is not pressed in another chord.

Chords of a circle are line segments that join two points on the circumference of the circle. In geometry, a common problem involving chords is to find the length of the chord when given the radius of the circle and the acute angle formed by the chord. To solve this problem, you can use the equation: Chord length = 2 × Radius × sin (Angle / 2). This equation can provide the answer to a variety of geometry problems involving chords. Additional equations and formulas can be used to solve more complex problems with chords, such as finding the length of two intersecting chords in a circle. With help from Plainmath you can gain a better understanding of how to use equations and formulas to solve a geometry problem with chords.