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  2. Intersecting chords theorem - Wikipedia

    en.wikipedia.org/wiki/Intersecting_chords_theorem

    The value of the two products in the chord theorem depends only on the distance of the intersection point S from the circle's center and is called the absolute value of the power of S; more precisely, it can be stated that: | | | | = | | | | = where r is the radius of the circle, and d is the distance between the center of the circle and the ...

  3. Circle - Wikipedia

    en.wikipedia.org/wiki/Circle

    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.

  4. Chord (geometry) - Wikipedia

    en.wikipedia.org/wiki/Chord_(geometry)

    Equal chords are subtended by equal angles from the center of the circle. A chord that passes through the center of a circle is called a diameter and is the longest chord of that specific circle. If the line extensions (secant lines) of chords AB and CD intersect at a point P, then their lengths satisfy AP·PB = CP·PD (power of a point theorem).

  5. Circular segment - Wikipedia

    en.wikipedia.org/wiki/Circular_segment

    A circular segment (in green) is enclosed between a secant/chord (the dashed line) and the arc whose endpoints equal the chord's (the arc shown above the green area). In geometry, a circular segment or disk segment (symbol: ⌓) is a region of a disk [1] which is "cut off" from the rest of the disk by a straight line.

  6. Tangent lines to circles - Wikipedia

    en.wikipedia.org/wiki/Tangent_lines_to_circles

    An inversion in their tangent point with respect to a circle of appropriate radius transforms the two touching given circles into two parallel lines, and the third given circle into another circle. Thus, the solutions may be found by sliding a circle of constant radius between two parallel lines until it contacts the transformed third circle.

  7. Degree of curvature - Wikipedia

    en.wikipedia.org/wiki/Degree_of_curvature

    Where degree of curvature is based on 100 units of arc length, the conversion between degree of curvature and radius is Dr = 18000/π ≈ 5729.57795, where D is degree and r is radius. Since rail routes have very large radii, they are laid out in chords, as the difference to the arc is inconsequential; this made work easier before electronic ...

  8. The ‘we listen and we don’t judge’ trend, unpacked by a ...

    www.aol.com/news/listen-don-t-judge-trend...

    The videos begin with both people saying, “We listen and we don’t judge” in unison. Many creators, however, seem to struggle with the not judging part, responding with shocked faces and open ...

  9. Hallade method - Wikipedia

    en.wikipedia.org/wiki/Hallade_method

    This formula is also true for other units of measurement such as in feet. The relationship of versine, chord and radius is derived from the Pythagorean theorem. Based on the diagram on the right: = We can replace OC with r (radius) minus v, OA with r and AC with L/2 (half a chord).