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Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
The external secant or external distance of a curved track section is the shortest distance between the track and the intersection of the tangent lines from the ends of the arc, which equals the radius times the trigonometric exsecant of half the central angle subtended by the arc, . [12] By comparison, the versed sine of a curved track ...
Rearranging the first equation gives a quadratic equation for .Solving that for gives = (^ ^) (¯ ^) (^ ^) (^ ^) (^ ^) (¯ (^ ^)) (^ ^) (^ ^) where (^ ^) = if ^ is a unit vector. If ‖ ^ ^ ‖ = the line is parallel to the axis, and there is no intersection, or the intersection is a line.
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The radius of a circle is perpendicular to the tangent line through its endpoint on the circle's circumference. Conversely, the perpendicular to a radius through the same endpoint is a tangent line. The resulting geometrical figure of circle and tangent line has a reflection symmetry about the axis of the radius.
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Dec. 8, police officers and firefighters responded to the incident at around 4:30 p.m., and the 12-year-old boy's body was recovered from the water about three hours later.
Equivalently, an inscribed angle is defined by two chords of the circle sharing an endpoint. The inscribed angle theorem relates the measure of an inscribed angle to that of the central angle subtending the same arc. The inscribed angle theorem appears as Proposition 20 in Book 3 of Euclid's Elements.