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The value of the two products in the chord theorem depends only on the distance of the intersection point S from the circle's center and is called the absolute value of the power of S; more precisely, it can be stated that: | | | | = | | | | = where r is the radius of the circle, and d is the distance between the center of the circle and the ...
The chord function is defined geometrically as shown in the picture. The chord of an angle is the length of the chord between two points on a unit circle separated by that central angle . The angle θ is taken in the positive sense and must lie in the interval 0 < θ ≤ π (radian measure).
In a right triangle, the circumcenter is the midpoint of the hypotenuse. In an isosceles triangle, the median, altitude, and perpendicular bisector from the base side and the angle bisector of the apex coincide with the Euler line and the axis of symmetry, and these coinciding lines go through the midpoint of the base side.
The tangent lines must be equal in length for any point on the radical axis: | | = | |. If P, T 1, T 2 lie on a common tangent, then P is the midpoint of ¯.. In Euclidean geometry, the radical axis of two non-concentric circles is the set of points whose power with respect to the circles are equal.
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 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 chord (in red) of length 0.3 on a sinusoidal function. The universal chord theorem guarantees the existence of chords of length 1/n for functions satisfying certain conditions.
The term chord function may refer to: Diatonic function – in music, the role of a chord in relation to a diatonic key; In mathematics, the length of a chord of a circle as a trigonometric function of the length of the corresponding arc; see in particular Ptolemy's table of chords .