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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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Columbus Medical Journal: A Magazine of Medicine and Surgery, Volume 28

1904 - 624 pages
...divide a straight line into five equal parts. 4. If two cords intersect within a circle prove that the product of the segments of one is equal to the product of the segments of the other. 5. Show how to construct a square equivalent to the difference of two given squares. 6. Show how to...
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Plane and Solid Geometry

Webster Wells, Walter Wilson Hart - Geometry - 1916 - 504 pages
...external segment will be 8 in. ? Ex. 73. If altitudes AD and BE of A ABC intersect at F, prove that the product of the segments of one is equal to the product of the segments of the other. (Apply § 284.) Ex. 74. If AD and BE are two altitudes of A ABC, then AD • BC = BE • AC. Ex. 75....
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Plane and Solid Geometry

William Betz - Geometry - 1916 - 536 pages
...46°, and ZB = 17°. Find the side It. 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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Third-year Mathematics for Secondary Schools

Ernst Rudolph Breslich - Logarithms - 1917 - 408 pages
...are in the same ratio as any two corresponding sides. [219] 430. If two chords of a circle intersect, the product of the segments of one is equal to the product of the segments of the other. [314] 431. If from a point without a circle a tangent and secant be drawn, the tangent is a mean proportional...
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 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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Plane Geometry

Mabel Sykes, Clarence Elmer Comstock - Geometry, Modern - 1918 - 576 pages
...are tangent internally. 13 FIG. 316 L_ IMPORTANT SPECIAL CASES INTERSECTING CHORDS 213. THEOREM 103. If two chords intersect within a circle, the product...equal to the product of the segments of the other. FIG. 317 Hypothesis: Circle O is any circle with the chords AB and CD intersecting at X so that a and...
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Solid Geometry

Claude Irwin Palmer - Geometry, Solid - 1918 - 192 pages
...squares of any two corresponding sides. PROPORTIONAL LINES CONNECTED WITH CIRCLES § 447. Theorem. If two chords intersect within a circle, the product...equal to the product of the segments of the other. § 450. Theorem. If a tangent and a secant are drawn to a circle from an external point, the tangent...
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Plane and Solid Geometry

Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry - 1918 - 460 pages
...similitude of the polygons ABCDE and A'B'C'D'E'. PROPORTIONAL LINES CONNECTED WITH CIRCLES 447. Theorem. // two chords intersect within a circle, the product...equal to the product of the segments of the other. Given circle 0 and the chords AB and CD intersecting at E. . To prove AE-BE = CE- DE. Proof. Draw AC...
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School Education, Volume 17

Education - 1898 - 634 pages
...Problem: to bisect a giren angle. 9. Show that if any two chords are drawn through a fixed point in a circle, the product of the segments of one is equal to the product of the segments of the other. 10. Show that two similar triangle« are to each other as the squares of their homologous sides. PLANE...
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High School Algebra Complete

Marquis Joseph Newell - 1920 - 424 pages
...and the total length of the other chord is 17 inches. Find the segments of the second chord. Note. If two chords intersect within a circle, the product of the segments of one equals the product of the segments of the other. 16. A number of boys bought a boat for $36. One of...
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