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" If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other. "
Plane Geometry - Page 148
by Arthur Schultze - 1901
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Bulletin

Education - 1921 - 1190 pages
...aides are proportional; (c) their sides are respectively proportional. 14. If two chords intersect in a circle, the product of the segments of one is equal to the product of the segments of the other. 15. The perimeters of two similar polygons have the same ratio as any two corresponding sides. 16....
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Bulletin, Issues 25-53

United States. Office of Education - 1921 - 1286 pages
...sides are proportional; (c) their sides are respectively proportional. 14. If two chords intersect in a circle, the product of the segments of one is equal to the product of the segments of the other. 15. The perimeters of two similar polygons have the same ratio as any two corresponding sides. 16....
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Solid Geometry

Mabel Sykes, Clarence Elmer Comstock - Geometry, Solid - 1922 - 236 pages
...necessary to find a third ratio to which each of the given ratios can be proved equal. THEOREM 103. If two chords intersect within a circle, the product...equal to the product of the segments of the other. THEOREM 104. If two secants intersect without a circle, the product of one secant and its external...
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The Reorganization of Mathematics in Secondary Education

National Committee on Mathematical Requirements - Mathematics - 1922 - 84 pages
...sides are proportional; (c) their sides are respectively proportional. 14. If two chords intersect in a circle, the product of the segments of one is equal to the product of the segments of the other. 15. The perimeters of two similar polygons have the same ratio as any two corresponding sides. 16....
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Railway Permanent Way: Dimensional Theory and Practice. A Manual for ...

William Hepworth, J. Thomas Lee - Railroad engineering - 1922 - 432 pages
...opposite segment. Angle BAC - Angle ADC. III., 35 (Fig. 13). If two lines in a circle cut each other, the product of the segments of one is equal to the product -of the segments of the other. ABxBC = DBxBE. III., 36 (Fig. 14). If from a point outside of a circle any line be drawn cutting the...
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General Mathematics, Book 2

Raleigh Schorling, William David Reeve - Mathematics - 1922 - 460 pages
...hypotenuse and the perpendicular from the vertex of the right angle upon the hypotenuse. 375. Theorem. If two chords intersect within a circle, the product of the segments of one chord is equal to the product of the segments of the other. FIG. 373 SUGGESTION. Draw AC and BD. EXERCISES...
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...in a common point or are parallel. [See applied problem 64, p. 297.] PROPOSITION XXX. THEOREM 320. If two chords intersect within a circle, the product...equal to the product of the segments of the other. Given in O 0, the chords AB and CD intersecting in E. To prove AE x EB = CE x ED. HINT. What is the...
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The Reorganization of Mathematics in Secondary Education: A Report of the ...

National Committee on Mathematical Requirements - Mathematics - 1923 - 680 pages
...both angles) in the one are equal to corresponding parts of the other." 14. If two chords intersect in a circle, the product of the segments of one is equal to the product of the segments of the other. 15. The perimeters of two similar polygons have the same ratio as any two corresponding sides. 16....
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Biennial Report, Volumes 16-20

1905 - 1094 pages
...two homologous sides. ">. To divide a line into extreme and mean ratio. в. If two cords intersect In a circle, the product of the segments of one Is equal to the product of the segments of the other. 7. The sum of the squares of two sides of a triangle is equal to twice the square of half the third...
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Plane Geometry

Walter Burton Ford, Charles Ammermann - Geometry, Modern - 1923 - 406 pages
...similar triangles. PART IV. PROPORTIONAL PROPERTIES OF CHORDS, SECANTS, AND TANGENTS 168. Theorem XI. // two chords intersect within a circle, the product of the segments of the one is equal to the product of the segments of the other. Given the chords AC and BD intersecting...
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