Problems in Geometry by A. Kutepov

By A. Kutepov

Best geometry and topology books

Plane Geometry and its Groups

San Francisco 1967 Holden-Day. octavo. , 288pp. , index, hardcover. positive in VG DJ, a number of small closed tears.

Additional resources for Problems in Geometry

Example text

At the point A lying on a given straight line a erect a perpendicular to this line. 2. From the point M not lying on a given straight line a drop a perpendicular to this line. 305. 1. Find the locus of points in space equidistant from a given point. 2. Find the locus of points in space equidistant from two given points. 3. Find the locus of points in space equidistant from three given points. 4. Find the locus of points in space equidistant from four given points. Consider all possible cases. 306.

Its end-points are found at distances of 6 cm and 4 cm from the plane. Find the angle between the given line segment and the plane. 353. 1. From a point located at a distance of a from the plane two straight lines are drawn inclined to the plane at angles of 30° and 45° and at a right angle to each CH. III. Determine the distance between the end-points of the inclined lines. 2. From a point located at a distance of a from a plane two inclined lines are drawn at an angle of 30° to the plane. Determine the angle between their projections if the distance between the end-points of the inclined lines is equal to 3a.

Particular Cases of Solving Oblique Triangles Notation: a, b, c = the sides of a triangle; A, B, C = = angles opposite them; S = area; 2p = perimeter; R = radius of the circumscribed circle; r = radius of the inscribed circle; ha, hb, h° = altitudes; la, 1b, 1° _ = bisectors. 7; B = 105°20'; C = 15°33. 205. 8; A = 70°24'; B = 50°16'; (3) a - b = 34; A = 108°; B = 28°. 4; A = 22°; B = 49°; . 206. 5 m; B = 114°50'; (3) a = 72; b = 52; A = 2B. 207. 8 m; (3) ha = 8; hb = 12; h° = 18. (2) S = 1460 m\$; CH.