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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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Annual Statistical Report

1911 - 864 pages
...= c — d :d. IX. Prcve: — If two chords intersect in a circle, the product M the segments of the one is equal to the product of the segments of the other. X. Construct a circle which shall pass through two given |v»ints and touch a given line. XI. The diagonals...
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The Teaching of Geometry

David Eugene Smith - Geometry - 1911 - 370 pages
...heavy pasteboard. THEOREM. If 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. COROLLARY. If from a point without a circle a secant is drawn, the product of the secant and its external...
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Plane Geometry

William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...46°, and £B = 17°. Find the side b. CIRCLES AND PROPORTIONAL LINES PROPOSITION XII. THEOREM 404. 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. Given in a circle two chords AB and CD...
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Plane Geometry

William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
...the side b. A = 46°, and /.B = 17°. CIRCLES AND PROPORTIONAL LINES PROPOSITION XII. THEOREM 404. 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. T) Given in a circle two chords AB and...
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Plane and Solid Geometry: Teacher's Edition

George Albert Wentworth, George Wentworth - Geometry - 1912 - 602 pages
...secants of a circle intersect within, on, or outside the circle, the product of the segments of the one is equal to the product of the segments of the other. 23. If four lines meet in a point so that the opposite angles are equal, these lines form two intersecting...
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 486 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 i To prove AE X EB = CE X ED. HINT. What is the means...
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Schultze and Sevenoak's Plane Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...meet in a common point or are parallel. [See applied problem 64, p. 297.] PROPOSITION XXX. THEOREM 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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Solid Geometry

Walter Burton Ford, Charles Ammerman - Geometry, Solid - 1913 - 176 pages
...corresponding sides. PART IV. PROPORTIONAL PROPERTIES OF CHORDS, SECANTS, AND TANGENTS 168. Theorem XI. If 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. 169. Theorem XII. If from a point without...
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Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...^.ADB. The &ABD and ECD are similar ; and the & BCD and AED are similar. PROPOSITION XXI. THEOREM 299. If 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 AB and CD, intersecting...
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Plane Geometry

Walter Burton Ford, Earle Raymond Hedrick - Geometry, Modern - 1913 - 272 pages
...SIMILARITY [III, § 168 PART IV. PROPORTIONAL PROPERTIES OF CHORDS, SECANTS, AND TANGENTS 168. Theorem XI. If 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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