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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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Essentials of Plane Geometry

David Eugene Smith - Geometry, Plane - 1923 - 314 pages
...Intersecting Chords 220. Theorem. If two chords of a circle intersect, the product of the segments of either one is equal to the product of the segments of the other. Given a O with the chords AB and CD, intersecting at P. Prove that PA"PB = PC. PD. Proof. Draw ACandBD....
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The Teaching of Mathematics in the Elementary and the Secondary School

Jacob William Albert Young - Mathematics - 1924 - 484 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. 1 6....
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Solving Geometric Originals, Issue 146

Frank Charles Touton - Geometry, Plane - 1924 - 134 pages
...Exercise 6 it must have been the purpose of the examiners to measure the knowledge of the theorem: "If two chords intersect within a circle, the product of the segments of one chord equals the product of the segments of the other." Now this general theorem is used by but 46.0...
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Plane and Solid Geometry

Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1923 - 414 pages
...polygons. PROPORTION 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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Essentials of Solid Geometry

David Eugene Smith - Geometry, Solid - 1924 - 256 pages
...same ratio as the radii. 3. If two chords of a circle intersect, the product of the segments of either one is equal to the product of the segments of the other. 4. The perpendicular from any point on a circle to a diameter of the circle is the mean proportional...
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A Geometry Reader

Julius J. H. Hayn - Geometry, Plane - 1925 - 328 pages
...polygons. 233. Prop. XXXV. Decomposition of similar polygons. Exercises Group 71 234. Prop. XXXVI. 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 chord. 236. Prop. XXXVII. If two secants...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1925 - 504 pages
...method of (309) and take the products of the means and extremes of the resulting proportion. Ex. 1. // two chords intersect within a circle, the product of the segments of one equals the product of the segments of the other. Ex. 2. If from any point E in the chord AB the perpendicular...
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Mathematics: Course of Study for Senior and Junior High Schools

Baltimore (Md.). Department of Education - Mathematics - 1924 - 182 pages
...corresponding sides. 4. a. If two chords intersect in a circle, the product of the segments of the one is equal to the product of the segments of the other. *b. If from a point without a circle, a tangent and a secant are drawn, the tangent is the mean proportional...
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The Reorganization of Mathematics in Secondary Education (part I): A ..., Part 1

National Committee on Mathematical Requirements - Mathematics - 1927 - 208 pages
...(c) their sides are respectively proportional. [59*, 60*, 61*, cd*] > 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. [67*] 15. The perimeters of two similar polygons have the same ratio as any two corresponding sidps....
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Examination Questions in Mathematics: Forth Series, 1916-1920

College Entrance Examination Board - Mathematics - 1920 - 108 pages
...congruent if the three sides of one are equal, respectively, to the three sides of the other. 2. a) Prove: If two chords intersect within a circle, the product...equal to the product of the segments of the other. b) A and B are two points on a railway curve which is an arc of a circle. If the length of the chord...
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