Extracting Arcs From Circle And The Properties

Extracting Arcs From Circle And The Properties

Introduction: Circle is a figure that people use in their daily lives. But no one thinks that this small figure has an endless number of properties. It is a completely different subject that kids need to learn in Mathematics. When you talk about a perfect circle, you will see that it has distinctive features. If you draw a line within a circle it becomes a whole different scenario. That line is termed a chord and it divides the circle into arcs. To calculate the length you will have to learn the arc length formula. There is an unlimited number of chords you can draw inside a circle.

Properties that kids need to understand:

You must have heard the term congruency in the chapter on triangles. There you had to prove certain conditions where the sides and angles are the same. Similarly, in circles, you need to prove that the radius is the same. Then automatically both of them will become congruent to each other. In case there are two chords with the same length, it will have a basic similarity. It is because the distance from their center will then be the same. If you bisect any chord with one line, it will go through the center as well.

Tangent and the properties

 If you draw a straight line outside the circle, you can make it meet at just one point on it. However, if it enters the circle then it will become a chord. When it stays outside and touches just one point, that line is called the tangent. That point will always be perpendicular to the center of the circle. Every point on the circle can have just one tangent. Two tangents can never originate from one point on it. Even if they look like that one of them will touch it at a different point. Now, draw a radius and the perpendicular to the center. You will find that both of them will be at a right angle to each other. Another theorem states that you can draw two tangents from one external point. However, both these tangents will look equal to each other as well.

What is the arc of the circle?

 Arc is nothing but an incomplete portion you can extract from a circle. You can make two arcs by just creating one chord inside. The bigger one is known as the major arc and the latter one is minor. If you calculate the length of a major arc, it should be greater than a semicircle. The only time when this does not happen is when the chord is diameter,

How to calculate it?

To find, you will need the value of the central angle first. As it is just length covered, the final answer will be in distance. The general formula for this problem will be, C(θ/360°). If you can calculate this then you will directly get the value for the length of the arc. C is also called the circumference or perimeter of the circle. For that, you will have to have to do 2 *3.14* r as well. It won’t be a problem as you will have the radius directly from the question.

Congruency with arc:

There is a way to find congruency with the help of arcs as well. For that, you need to extend it and find the central angle with it. If both the arc angles are the same, then the circle will be congruent as well. If you subtend the angle at any other point, it will be half the central angle.

Circles and arcs are some of the most interesting chapters to learn in Maths. You can visit website that is descriptive such as the Cuemath classes and you can get more information regarding circles and other math topics.

You May Also Like

WP2Social Auto Publish Powered By : XYZScripts.com