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 148by Arthur Schultze - 1901Full view - About this book
| 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... | |
| 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... | |
| 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.... | |
| 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.... | |
| 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.... | |
| 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... | |
| 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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