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This property follows directly from applying the chord theorem to a third chord going through S and the circle's center M (see drawing). The theorem can be proven using similar triangles (via the inscribed-angle theorem).
Pappus's hexagon theorem states that, if a hexagon AbCaBc is drawn in such a way that vertices a, b and c lie on a line and vertices A, B and C lie on a second line, then each two opposite sides of the hexagon lie on two lines that meet in a point and the three points constructed in this way are collinear.
In a parallelogram with a point on the diagonal , the parallel to through intersects the side in and the side in .Similarly the parallel to the side through intersects the side in and the side in .
The small-angle approximations can be used to approximate the values of the main trigonometric functions, provided that the angle in question is small and is measured in radians: sin θ ≈ θ cos θ ≈ 1 − θ 2 2 ≈ 1 tan θ ≈ θ {\displaystyle {\begin{aligned}\sin \theta &\approx \theta \\\cos \theta &\approx 1-{\frac ...
Analogously, a line segment PD through some point D on AB extended bisects the corresponding exterior angle BPQ where Q is on AP extended. Since the interior and exterior angles sum to 180 degrees, the angle CPD is exactly 90 degrees; that is, a right angle. The set of points P such that angle CPD is a right angle forms a circle, of which CD is ...
In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles. According to the law, = = =, where a, b, and c are the lengths of the sides of a triangle, and α, β, and γ are the opposite angles (see figure 2), while R is the radius of the triangle's circumcircle.
Angle AOB is a central angle. A central angle is an angle whose apex (vertex) is the center O of a circle and whose legs (sides) are radii intersecting the circle in two distinct points A and B. Central angles are subtended by an arc between those two points, and the arc length is the central angle of a circle of radius one (measured in radians). [1]
Colors that can be produced by visible light of a narrow band of wavelengths (monochromatic light) are called pure spectral colors.The various color ranges indicated in the illustration are an approximation: The spectrum is continuous, with no clear boundaries between one color and the next.