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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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Plane and Solid Geometry

Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1913 - 376 pages
...168 FIG. 122 Why? 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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Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 491 pages
...diagonals is equal to the sum of the products of the opposite sides. 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 CZ>, intersecting...
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Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...PROPOSITION XXI. THEOREM 299. If tivo' 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 at P. To prove that PAxPB=PCx PD. Proof. Dra-w AC and BD....
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Plane Geometry

Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry, Plane - 1915 - 320 pages
...II EA, and prove that A'B'C'D'E'^ABCDE. 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 O and the chords AB and CD intersecting at E. To prove AE- BE =CE'-DE. Proof. Draw AC...
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Plane Geometry

Webster Wells, Walter Wilson Hart - Geometry, Plane - 1915 - 330 pages
...AD AB BC AC XW XY YZ XZ PROPOSITION IX. THEOREM 283. If two chords are drawn through a fixed point within a circle, the product of the segments of one...equal to the product of the segments of the other. Hypothesis. AB and CD are any two chords of O 0 intersecting at point P. Conclusion. AP -PB = DP- PC....
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Plane Geometry

John Wesley Young, Albert John Schwartz - Geometry, Modern - 1915 - 248 pages
...rectangle. 426. PROPORTIONAL SEGMENTS PROPORTIONAL LINE SEGMENTS 432. THEOREM. 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. FIG. 200. Given the circle with two chords AB and CD intersecting in P. To prove that AP x BP = CP...
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Plane and Solid Geometry

Webster Wells, Walter Wilson Hart - Geometry - 1916 - 490 pages
...sides of the triangles. PROPOSITION IX. THEOREM 283. If two chords are drawn through a fixed point within a circle, the product of the segments of one...equal to the product of the segments of the other. Hypothesis. AB and CD are any two chords of O 0 intersecting at point P. Conclusion. AP-PB = DP.PC....
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Plane Geometry

John Charles Stone, James Franklin Millis - Geometry - 1916 - 298 pages
...square of the hypotenuse. To prove that 4(AE* + BD*) = 5 AB*. 200. Theorem. — If two chords intersect, the product of the segments of one is equal to the product of the segments of the other. C Hypothesis. Chords AB and CD intersect at a point 0. Conclusion. A 0 x OB = CO x OD. Suggestion....
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Solid Geometry

John Charles Stone, James Franklin Millis - Geometry, Solid - 1916 - 196 pages
...of the hypotenuse is equal to the sum of the squares of the legs. 200. If two chords intersect, the product of the segments of one is equal to the product of the segments of the other. 215. Parallelograms having equal altitudes and equal bases are equal. 228. Two triangles having...
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Second-year Mathematics for Secondary Schools

Ernst Rudolph Breslich - Mathematics - 1916 - 392 pages
...Fig. 263). Summary 318. The following theorems were proved: 1. // two chords of a circle intersect, the product of the segments of one is equal to the product of the segments of the other. 2. If from a point without a circle a tangent and secant be drawn the tangent is a mean proportional...
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