Class: 10th | Mathematics (FBISE) | Lecture # | Unit #12 | Theorem #3 | Angles in a Circle | скачать в хорошем качестве

Class: 10th | Mathematics (FBISE) | Lecture # | Unit #12 | Theorem #3 | Angles in a Circle |

Class: 10th | Mathematics (FBISE) | Lecture # | Unit #12 | Theorem #3 | Angles in a Circle | The angle • in a semi-circle is a right angle, • in a segment greater than a semi-circle is less than a right angle, • in a segment less than a semi-circle is greater than a right 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 | The line segment AC is the diameter of the semicircle. The inscribed angle is formed by drawing a line from each end of the diameter to any point on the semicircle. No matter where you do this, the angle formed is always 90°. Drag the point B and convince yourself this is so. This is true regardless of the size of the semicircle. Drag points A and C to see that this is true. The triangle formed by the diameter and the inscribed angle (triangle ABC above) is always a right triangle. This is a particular case of Thales Theorem, which applies to an entire circle, not just a semicircle. Thales Theorem states that any diameter of a circle subtends a right angle to any point on the circle. (see figure on right). No matter where the point is, the triangle formed is always a right triangle. See Thales Theorem for an interactive animation of this concept. QP is a major arc and Angle PSQ is the angle formed by it in the alternate segment. We know that, the angle subtended by an arc at the centre is twice the angle subtended by it at any point of the alternate segment of the circle. ∴ 2 Angle PSQ = m ⇒ 2 Angle PSQ = 360° – m ⇒ 2 Angle PSQ = 360° – Angle POQ ⇒ 2 Angle PSQ = 360° – 180° (∵ Angle POQ is less than 180°) ⇒ 2 Angle PSQ is greater than 180° ⇒ Angle PSQ is greater than 90° In geometry and trigonometry, a right angle is an angle of exactly 90 degrees or π/2 radians corresponding to a quarter turn. If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles. The term is a calque of Latin angulus rectus; here rectus means "upright", referring to the vertical perpendicular to a horizontal base line. Closely related and important geometrical concepts are perpendicular lines, meaning lines that form right angles at their point of intersection, and orthogonality, which is the property of forming right angles, usually applied to vectors. The presence of a right angle in a triangle is the defining factor for right triangles, making the right angle basic to trigonometry.