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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.
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").
A curve is simple if it is the image of an interval or a circle by an injective continuous function. In other words, if a curve is defined by a continuous function γ {\displaystyle \gamma } with an interval as a domain, the curve is simple if and only if any two different points of the interval have different images, except, possibly, if the ...
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 ...
The signed curvature (or bend) of a circle is defined as = /, where is its radius. The larger a circle, the smaller is the magnitude of its curvature, and vice versa. The sign in k = ± 1 / r {\displaystyle k=\pm 1/r} (represented by the ± {\displaystyle \pm } symbol) is positive for a circle that is externally tangent to the other circles.
Though most people say 'Looks like we're not in Kansas anymore,' or 'Toto, I don't think we're in Kansas anymore,' those quotes aren't quite right. Dorothy actually says 'Toto, I've a feeling we ...
Monge's theorem states that the three such points given by the three pairs of circles always lie in a straight line. In the case of two of the circles being of equal size, the two external tangent lines are parallel. In this case Monge's theorem asserts that the other two intersection points must lie on a line parallel to those two external ...
Hiking is one of those “hobbies” that you either love or hate. On the one hand, being cold, tired and beset by mosquitoes. On the other, health, mental wellbeing and some time alone in nature.