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In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal.
A chord (from the Latin chorda, meaning "bowstring") of a circle is a straight line segment whose endpoints both lie on a circular arc. If a chord were to be extended infinitely on both directions into a line, the object is a secant line. The perpendicular line passing through the chord's midpoint is called sagitta (Latin for "arrow").
Line DE bisects line AB at D, line EF is a perpendicular bisector of segment AD at C, and line EF is the interior bisector of right angle AED. In geometry, bisection is the division of something into two equal or congruent parts (having the same shape and size). Usually it involves a bisecting line, also called a bisector.
If the radii are equal, the radical axis is the line segment bisector of M 1, M 2. In any case the radical axis is a line perpendicular to ¯. On notations. The notation radical axis was used by the French mathematician M. Chasles as axe radical. [1] J.V. Poncelet used chorde ideale. [2]
If a bicentric quadrilateral has tangency chords k, l and diagonals p, q, then it has area [8]: p.129 = +. If k, l are the tangency chords and m, n are the bimedians of the quadrilateral, then the area can be calculated using the formula [9]
A perpendicular line from the centre of a horocycle bisects the chord. The line segment through the centre bisecting a chord is perpendicular to the chord. A line drawn perpendicular to a radius through the end point of the radius lying on the horocycle is a tangent to the horocycle. A line drawn perpendicular to a tangent through the point of ...
The sagitta (also known as the versine) is a line segment drawn perpendicular to a chord, between the midpoint of that chord and the arc of the circle. Given the length y of a chord and the length x of the sagitta, the Pythagorean theorem can be used to calculate the radius of the unique circle that will fit around the two lines: r = y 2 8 x ...
Common lines and line segments on a circle, including a secant. A straight line can intersect a circle at zero, one, or two points. A line with intersections at two points is called a secant line, at one point a tangent line and at no points an exterior line. A chord is the line segment that joins two distinct points of a circle. A chord is ...