![]() ![]() Sector: A portion of a circle resembling a 'slice of pizza'. Greater than 180 degrees.Īngle of centre: An angle at the centre of a triangle between two lines that intersect with the perimeter.Īngle at circumference on minor arc: The smaller of 2 angles when a circle is split into 2 uneven parts. ![]() Point of contact: Where a tangent touches a circle.Īrc: A part of the curve along the perimeter of a circle.Īngle on major arc: The larger of 2 angles when a circle is split into 2 uneven parts. Tangent: A tangent to a circle is a straight line which touches the circle at only one point (so it does not cross the circle - it just touches it). Segment: A part of the circle separated from the rest of a circle by a chord. A diameter is the longest chord possible. Radius: Any straight line that originates at the centre of a circle and ends at the perimeter.Ĭhord: A straight line whose ends are on the perimeter of a circle. One advantage of this choice of radius was that he could very accurately approximate the chord of a small angle as the angle itself.This section of Revision Maths defines many terms in relation to circles, including: Circumference, Diameter, Radius, Chord, Segment, Tangent, Point of contact, Arc, Angles on major and minor arcs, Angle of Centre and Sectors.Ĭircumference: The circumference of a circle is the distance around it.ĭiameter: Any straight line that passes through the centre of the circle to two points on the perimeter. It was then a simple matter of scaling to determine the necessary chord for any circle. ![]() Ancient chord tables typically used a large value for the radius of the circle, and reported the chords for this circle. The half-angle identity greatly expedites the creation of chord tables. The chord function satisfies many identities analogous to well-known modern ones: Hipparchus is purported to have written a twelve volume work on chords, not extant, so presumably a great deal was known about them. Much as modern trigonometry is built on the sine function, ancient trigonometry was built on the chord function. The last step uses the half-angle formula. By taking one of the points to be zero, it can easily be related to the modern sine function: So, chord is the line segment that joins the two points on the. Diameter is the longest chord of the circle. The chords of a circle that are equal in length are always equidistant from the center. Perpendicular from the center of a circle to a chord bisects a chord. The chord of an angle is the length of the chord between two points on a unit circle separated by that angle. The chords that are equal in length subtend equal angles at the center. The chord of a circle that passes through the center of the circle. ![]() Theorem 3: If a line is drawn parallel to one side of a triangle to intersect the midpoints of the other two sides, then the two sides are divided in the same ratio. Now Let’s learn some advanced level Triangle Theorems. The chord function is defined geometrically as in the picture to the left. A chord of the circle is the straight line segment which has both its endpoint on the circle. XY XZ Two sides of the triangle are equal Hence, Y Z. The first known trigonometric table, compiled by Hipparchus, tabulated the value of the Chord function for every 7.5 degrees. Chords were used extensively in the early development of trigonometry. ![]()
0 Comments
Leave a Reply. |
Details
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |