Angle Subtended by a Chord at a Point An angle subtended by a chord at a point is the angle formed by the chord and its intercepted arc. In other words, it...
Angle Subtended by a Chord at a Point
An angle subtended by a chord at a point is the angle formed by the chord and its intercepted arc. In other words, it is the angle formed by the arc of the chord intercepted by the radius of the circle at the point.
Examples:
If a chord CD intersects the circumference of a circle at points A and B, then the angle subtended by CD at point C is equal to the angle subtended by CD at point D.
If a chord passes through the center of a circle, then the angle subtended by the chord at any point on the circle will be equal to 180 degrees.
If a chord intersects the circumference of a circle at two points, then the angle subtended by the chord at the point where it intersects the circumference will be equal to the sum of the angles subtended by the chord at the two endpoints of the arc.
Formal Definition:
The angle subtended by a chord at a point is the angle formed by the chord and its intercepted arc. It is expressed in degrees, radians, or any other suitable unit.
Applications:
Angles subtended by chords have a wide range of applications in geometry and trigonometry. For example, they can be used to calculate the area of a circle, the perimeter of a circle, and the angles of triangles and other shapes