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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

## 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...

## 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....

## 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...

## 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...

## 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...

## 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...

## 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...

## 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...