TAILIEUCHUNG - Handbook of mathematics for engineers and scienteists part 14

An angle bisector of a triangle is a line segment between a vertex and a point of the opposite side and dividing the angle at that vertex into two equal parts (Fig. ). The three angle bisectors intersect in a single point lying strictly inside the triangle. | . Solid Geometry 59 a b Figure . A segment a and an annulus b . be the inner radius the radius of the inner bounding circle . Then the area of the annulus is given by the formula S n R2 - r2 n D2 - d2 2np6 where D 2R and d 2r are the outer and inner diameters p 2 R r is the midradius and 6 R - r is the width of the annulus. The area of the part of the annulus contained in a sector of central angle given in degrees see Fig. is given by the formula S R2 - r2 - n D2 - d2 n P5. 360 1440 180 . Solid Geometry . Straight Lines Planes and Angles in Space . Mutual arrangement of straight lines and planes. 1 . Two distinct straight lines lying in a single plane either have exactly one point of intersection or do not meet at all. In the latter case they are said to be parallel. If two straight lines do not lie in a single plane then they are called skew lines. The angle between skew lines is determined as the angle between lines parallel to them and lying in a single plane Fig. . The distance between skew lines is the length of the straight line segment that meets both lines and is perpendicular to them. b Figure . The angle between skew lines a . The angle between a line and a plane b . 2 . Two distinct planes either intersect in a straight line or do not have common points. In the latter case they are said to be parallel. Coinciding planes are also assumed to be parallel. If two planes are perpendicular to a single straight line or each of them contains a pair of intersecting straight lines parallel to the corresponding lines in the other pair then the planes are parallel. 60 Elementary Geometry 3 . A straight line either entirely lies in the plane meets the plane at a single point or has no common points with the plane. In the last case the line is said to be parallel to the plane. The angle between a straight line and a plane is equal to the angle between the line and its projection onto the plane Fig. . If a .

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