Class: 10th | Mathematics (FBISE) | Lecture # | Unit #11 | Theorem #1 | Chords and Arcs | скачать в хорошем качестве

Class: 10th | Mathematics (FBISE) | Lecture # | Unit #11 | Theorem #1 | Chords and Arcs |

Class: 10th | Mathematics (FBISE) | Lecture # | Unit #11 | Chords and Arcs | Theorem #1 | If two arcs of a circle (or of congruent circles) are congruent then the corresponding chords are equal | Dear viewers, it is my pleasure to deliver you mathematics tutorials in simple and native language so that you can get it easily | #MathsMadeEasy is a channel where you can improve your #Mathematics | This is an education channel where maths made easy will try to solve your problems | Students may send the problems they are facing through comments | Chord of a Circle Definition The chord of a circle can be defined as the line segment joining any two points on the circumference of the circle. It should be noted that the diameter is the longest chord of a circle which passes through the center of the circle. The figure below depicts a circle and its chord. Chord of a Circle Theorems If we try to establish a relationship between different chords and the angle subtended by them in the center of the circle, we see that the longer chord subtends a greater angle at the center. Similarly, two chords of equal length subtend equal angle at the center. Let us try to prove this statement. Theorem 1: Equal Chords Equal Angles Theorem Statement: Chords which are equal in length subtend equal angles at the center of the circle. Theorem 2: Equal Angles Equal Chords Theorem (Converse of Theorem 1) Statement: If the angles subtended by the chords of a circle are equal in measure, then the length of the chords is equal. Theorem 3: Equal Chords Equidistant from Center Theorem Statement: Equal chords of a circle are equidistant from the center of the circle. Arc Length Formula Arc length formula is used to calculate the measure of the distance along the curved line making up the arc (a segment of a circle). In simple words, the distance that runs through the curved line of the circle making up the arc is known as the arc length. It should be noted that the arc length is longer than the straight line distance between its endpoints. Arc In Mathematics, an “arc” is a smooth curve joining two endpoints. In general, an arc is one of the portions of a circle. It is basically a part of the circumference of a circle. Arc is a part of a curve. An arc can be a portion of some other curved shapes like an ellipse but mostly refers to a circle. In this article, let us discuss the arc of a circle, measures and arc length formula in a detailed way.