The question cannot be answered because it is not clear what is to be proved.
The term "subtended" refers to the angle formed at a specific point by two lines or segments extending to meet at that point. In geometry, it often describes how an angle is formed by two radii of a circle meeting the circumference, with the arc between them being subtended by that angle. Essentially, it conveys the relationship between angles and the figures they encompass.
Assume you mean the chord of a circle? If the angle between the two radii from the ends of the chord is A, and the radius of the circle is R, the chord length L will be L = 2RsinA/2. You can prove this easily by joining the point bisecting the chord to the centre, you then have two rightangled triangles, with an included angle of A/2, and an opposite side of L/2. So sinA/2 = L/2R.
Yes, the measure of a tangent-chord angle is indeed twice the measure of the intercepted arc. This is a key property of circles in geometry. Specifically, if a tangent and a chord intersect at a point on the circle, the angle formed between them is equal to half the measure of the arc that lies between the points where the chord intersects the circle.
150
To determine the measure of angle E when lines DE and EF are tangent to circle O, we use the property that the angle formed between a tangent and a radius drawn to the point of tangency is equal to the angle subtended by the chord at the circumference. If the diagram provided shows specific angles or other relevant information, please refer to those for a numerical answer. Otherwise, without additional data, we cannot provide a precise measure for angle E.
The term "subtended" refers to the angle formed at a specific point by two lines or segments extending to meet at that point. In geometry, it often describes how an angle is formed by two radii of a circle meeting the circumference, with the arc between them being subtended by that angle. Essentially, it conveys the relationship between angles and the figures they encompass.
Assume you mean the chord of a circle? If the angle between the two radii from the ends of the chord is A, and the radius of the circle is R, the chord length L will be L = 2RsinA/2. You can prove this easily by joining the point bisecting the chord to the centre, you then have two rightangled triangles, with an included angle of A/2, and an opposite side of L/2. So sinA/2 = L/2R.
Radius: A line from the center of a circle to a point on the circle. Central Angle: The angle subtended at the center of a circle by two given points on the circle.
It is 360 degrees because angles around a point add up to 360 degrees
Yes, the measure of a tangent-chord angle is indeed twice the measure of the intercepted arc. This is a key property of circles in geometry. Specifically, if a tangent and a chord intersect at a point on the circle, the angle formed between them is equal to half the measure of the arc that lies between the points where the chord intersects the circle.
150
4/9*pi*r where r is the radius of the circle.
this term is often confused with angle of field and field of view. The angle of view is the (diagonal) angle subtended by the scene captured in the photograph. This establishes the disc of best definition required for the lens. The angle of field is the angle subtended at the lens rear nodal point by the diagonal of the format itself. In a rectilinear image this is the same as the angle of view, but not for anamorphic images such as those produced by fisheye lenses. 'Field of view' simply describes the area covered in a scene. For example, although the angle of view of a fisheye lens is 180 degrees, its angle of field may be as low as 90 degrees. The field of view may be described as 'horizon to horizon'. For a standard (prime) lens the angle of field is typically 50-55 degrees, the same as the angle of view, and the field of view is roughly the same as that of the eye in a normal viewing of a scene or a picture.
A chord is a straight line that extends from one point of the circumference of a circle to another point on the circumference and the diameter of a circle is its largest chord
You are probably thinking of latitude, which shows distance from the equator as the angle subtended by the arc between the place and the nearest point on the equator. For instance, the latitude of London, United Kingdom, is 51.5 degrees N.
a diameter is always a chord because a chord always goes from one point of the circle to the other and a a diameter goes from one point to the midpoint
The radius of the circle that is perpendicular to a chord intersects the chord at its midpoint, so it is said to bisect the chord.