![circle geometry circle geometry](http://www.a-levelmathstutor.com/images/coord-geom/circle03.jpg)
![circle geometry circle geometry](http://2.bp.blogspot.com/-hLe8gaLtxNo/Un-BwTEuPoI/AAAAAAAAMDY/A7fRJsXFiJs/s1600/cds+exam+circle-theorums.png)
Circular segment - the part of the sector that remains after removing the triangle formed by the center of the circle and the two endpoints of the circular arc on the boundary.The chord function can be related to the modern sine function, by taking one of the points to be (1,0), and the other point to be ( cos θ, sin θ), and then using the Pythagorean theorem to calculate the chord length: crd θ = ( 1 − cos θ ) 2 + sin 2 θ = 2 − 2 cos θ = 2 sin ( θ 2 ). All points on the circle, by definition, are equidistant from the center, so no matter which point on the circle is the endpoint of a given radius, it is congruent to any other radius. The angle θ is taken in the positive sense and must lie in the interval 0 < θ ≤ π (radian measure). A radius has one endpoint on the center and one on the circle. The chord of an angle is the length of the chord between two points on a unit circle separated by that central angle. The chord function is defined geometrically as shown in the picture. The circle was of diameter 120, and the chord lengths are accurate to two base-60 digits after the integer part. The circumference (meaning 'all the way around') of a circle is the line that goes around the centre of the circle. The diameter of a circle is equal to twice its radius (d equals 2 times r). where (theta,alpha) are polar coordinates of any point on the circle and (R,alpha) are polar coordinates of the center of the circle. All points on the edge of the circle are at the same distance from the center. Equation of circle from analytic geometry. A apply theorems about circles, including relationships among angles, radii, chords, tangents, and secants, to solve non-contextual problems Arcs and chords (G-U.8) Tangent lines (G-U. A circle is a round, two-dimensional shape. And here is the really cool thing: When we divide the circumference by the diameter we get 3.141592654. The Circumference is the distance once around the circle. The Diameter goes straight across the circle, through the center. In the second century AD, Ptolemy of Alexandria compiled a more extensive table of chords in his book on astronomy, giving the value of the chord for angles ranging from 1 / 2 to 180 degrees by increments of 1 / 2 degree. 12 The student uses the process skills to understand geometric relationships and apply theorems and equations about circles. The Radius is the distance from the center outwards. The first known trigonometric table, compiled by Hipparchus, tabulated the value of the chord function for every 7 + 1 / 2 degrees. Chords were used extensively in the early development of trigonometry.