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In trigonometry, the law of tangents or tangent rule [1] is a statement about the relationship between the tangents of two angles of a triangle and the lengths of the opposing sides. In Figure 1, a , b , and c are the lengths of the three sides of the triangle, and α , β , and γ are the angles opposite those three respective sides.
A tangential quadrilateral is usually defined as a convex quadrilateral for which all four sides are tangent to the same inscribed circle. Pitot's theorem states that, for these quadrilaterals, the two sums of lengths of opposite sides are the same. Both sums of lengths equal the semiperimeter of the quadrilateral. [2]
Kissing circles. Given three mutually tangent circles (black), there are, in general, two possible answers (red) as to what radius a fourth tangent circle can have. In geometry, Descartes' theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic equation. By solving this ...
By the power-of-a-point theorem, the product of lengths PM · PN for any ray PMN equals to the square of PT, the length of the tangent line segment (red). No tangent line can be drawn through a point within a circle, since any such line must be a secant line. However, two tangent lines can be drawn to a circle from a point P outside of the circle.
Ex-tangential quadrilateral – Convex 4-sided polygon whose sidelines are all tangent to an outside circle; Harcourt's theorem – Area of a triangle from its sides and vertex distances to any line tangent to its incircle; Circumconic and inconic – Conic section that passes through the vertices of a triangle or is tangent to its sides
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New details about a study that warned against black plastic spatulas and other kitchen tools have come out. (Getty Creative) (Анатолий Тушенцов via Getty Images)
When an equidiagonal kite has side lengths less than or equal to its diagonals, like this one or the square, it is one of the quadrilaterals with the greatest ratio of area to diameter. [21] A kite with three 108° angles and one 36° angle forms the convex hull of the lute of Pythagoras, a fractal made of nested pentagrams. [22]