Class: 10th | Mathematics (FBISE) | Lecture # | Unit #12 | Central angle and Circum angle | скачать в хорошем качестве

Class: 10th | Mathematics (FBISE) | Lecture # | Unit #12 | Central angle and Circum angle |

Class: 10th | Mathematics (FBISE) | Lecture # | Unit #12 | Central angle and Circum angle (Inscribed angle) | Mathematics Science Group | 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 | A central angle is an angle whose vertex is the centre of a circle and whose arms are radii intersecting the circle at two distinct points. #CentralAngles are subtended by an arc between these two points. The central angle is given by the formula given below. Central angle θ = (arc length × 3600)/2πr Here r is the radius of the circle. #InscribedAngles An inscribed angle in a circle is formed by two chords that have a common end point on the circle. This common end point is the vertex of the angle. In geometry, an inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle. It can also be defined as the angle subtended at a point on the circle by two given points on the circle. Equivalently, an inscribed angle is defined by two chords of the circle sharing an endpoint. The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle. Therefore, the angle does not change as its vertex is moved to different positions on the circle. Applications The inscribed angle theorem is used in many proofs of elementary Euclidean geometry of the plane. A special case of the theorem is Thales' theorem, which states that the angle subtended by a diameter is always 90°, i.e., a right angle. As a consequence of the theorem, opposite angles of cyclic quadrilaterals sum to 180°; conversely, any quadrilateral for which this is true can be inscribed in a circle. As another example, the inscribed angle theorem is the basis for several theorems related to the power of a point with respect to a circle. Further, it allows one to prove that when two chords intersect in a circle, the products of the lengths of their pieces are equal. Inscribed angle theorems for ellipses, hyperbolas and parabolas Inscribed angle theorems exist for ellipses, hyperbolas and parabolas, too. The essential differences are the measurements of an angle. (An angle is considered a pair of intersecting lines.)