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Tangent lines to circles. In Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior. Tangent lines to circles form the subject of several theorems, and play an important role in many geometrical constructions and proofs.
A tangent, a chord, and a secant to a circle. The intuitive notion that a tangent line "touches" a curve can be made more explicit by considering the sequence of straight lines (secant lines) passing through two points, A and B, those that lie on the function curve. The tangent at A is the limit when point B approximates or tends to A. The ...
The tangent line to the unit circle at the point A, is perpendicular to , and intersects the y - and x-axes at points = (,) and = (,). The coordinates of these points give the values of all trigonometric functions for any arbitrary real value of θ in the following manner.
Thales's theorem. Thales’ theorem: if AC is a diameter and B is a point on the diameter's circle, the angle ∠ ABC is a right angle. In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ∠ ABC is a right angle. Thales's theorem is a special case of the inscribed ...
The center of the incircle is a triangle center called the triangle's incenter. [1] An excircle or escribed circle[2] of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two. Every triangle has three distinct excircles, each tangent to one of the triangle's sides.
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
The angle between the horizontal line and the shown diagonal is 1 2 (a + b). This is a geometric way to prove the particular tangent half-angle formula that says tan 1 2 (a + b) = (sin a + sin b) / (cos a + cos b). The formulae sin 1 2 (a + b) and cos 1 2 (a + b) are the ratios of the actual distances to the length ...
In geometry, tangent circles (also known as kissing circles) are circles in a common plane that intersect in a single point. There are two types of tangency: internal and external. Many problems and constructions in geometry are related to tangent circles; such problems often have real-life applications such as trilateration and maximizing the ...