 | Walter Burton Ford, Charles Ammerman - Geometry, Solid - 1913 - 176 pages
...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 a circle a secant and a tangent are drawn, the tangent is... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1913 - 376 pages
...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... | |
 | 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... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Solid - 1913 - 184 pages
...corresponding sides. PART IV. PROPORTIONAL PROPERTIES OF CHORDS, SECANTS, AND TANGENTS 168. Theorem XL 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... | |
 | Walter Burton Ford, Earle Raymond Hedrick - Geometry, Modern - 1913 - 272 pages
...[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... | |
 | 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... | |
 | 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.... | |
 | 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... | |
 | 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.... | |
 | 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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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. 
