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The midpoint method computes + so that the red chord is approximately parallel to the tangent line at the midpoint (the green line). In numerical analysis , a branch of applied mathematics , the midpoint method is a one-step method for numerically solving the differential equation ,
Every triangle has an inscribed ellipse, called its Steiner inellipse, that is internally tangent to the triangle at the midpoints of all its sides. This ellipse is centered at the triangle's centroid, and it has the largest area of any ellipse inscribed in the triangle. In a right triangle, the circumcenter is the midpoint of the hypotenuse.
A tangent line t to a circle C intersects the circle at a single point T. For comparison, secant lines intersect a circle at two points, whereas another line may not intersect a circle at all. This property of tangent lines is preserved under many geometrical transformations, such as scalings, rotation, translations, inversions, and map ...
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.
The angle between a chord and the tangent at one of its endpoints is equal to one half the angle subtended at the centre of the circle, on the opposite side of the chord (tangent chord angle). If the angle subtended by the chord at the centre is 90°, then ℓ = r √2, where ℓ is the length of the chord, and r is the radius of the circle.
The midpoint of the line segment from each vertex of the triangle to the orthocenter ... The nine point circle and the 16 tangent circles of the orthocentric system.
Draw a line tangent to the circle which passes through the given non-central point. Draw a horizontal line through that point of tangency and find its intersection with the vertical line. The midpoint between that intersection and the given non-central point is the center of the model circle.
In computer graphics, the midpoint circle algorithm is an algorithm used to determine the points needed for rasterizing a circle. It's a generalization of Bresenham's line algorithm . The algorithm can be further generalized to conic sections .