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
| Isaac Newton Failor - Geometry - 1906 - 440 pages
...= 2 ( £ ) + 2 m2. Ax. 1 W (1) - (2) gives 62 - c2 = 2 an. Ax. 4 170 PROPOSITION TCXTU THEOREM 377 **If two chords intersect within a circle, the product...equal to the product of the segments of the other.** HYPOTHESIS. The chords AB and CD intersect at P. CONCLUSION. PA x PB = PC x PD. PROOF Draw AC and DB.... | |
| Isaac Newton Failor - Geometry - 1906 - 431 pages
...c" = 2 (5) + 2ms. (1) - (2) gives b2 - c2 = 2 ew. § 373 Ax. 1 Ax. 4 PROPOSITION XXXI. THEOREM 377 **If two chords intersect within a circle, the product...equal to the product of the segments of the other.** HYPOTHESIS. The chords AB and CD intersect at P. CONCLUSION. PA x PB = PC x PD. PROOF Draw AC and DB.... | |
| International Correspondence Schools - Building - 1906 - 634 pages
...Tr* = PA* and lPT% = />Cx hence, PAxPB=PCxPD FIG. 23 31. If any two chords be drawn through a point **within a circle, the product of the segments of one...equal to the product of the segments of the other.** In Fig. 24, the angles D and Ft, being measured by one-half the arc AC, are equal. The angles B PC... | |
| Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...AP PD .-._ — _, or AP X PB = CP X PD. CP PB 363. Exercise. If two line segments intersect so that **the product of the segments of one is equal to the product of the segments of the other,** their four extremities lie on a circumference. SUGGESTION. Pass a circumference through three of the... | |
| George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 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 CD, intersecting... | |
| William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 284 pages
...medians of a triangle whose sides are, respectively, 12, 14, and 16. PROPOSITION XLIII. THEOREM. 405. **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 two chords, AB and CD, intersecting... | |
| William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 286 pages
...PROPOSITION XLIII. THEOREM. 405. 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 two chords, AB and CD, intersecting within the circle at P. To prove AP xBP=CPx DP. Proof Draw... | |
| Geometry, Plane - 1911 - 192 pages
...intersect at E, prove that AE = ED and BE = EC. 6. 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.** 7. AD and BC are the parallel sides of a trapezoid ABCD, whose diagonals intersect at E. If F is the... | |
| Robert Louis Short, William Harris Elson - Mathematics - 1911 - 216 pages
...CHAPTER XVI Applications of the Circle. Proportionals THEOREM LXXIII 268. If two chords intersect, **the product of the segments of one is equal to the product of the segments of the other.** Draw a circle; draw chord AB and chord CD intersecting at P. We have Given chords AB and CD intersecting... | |
| David Eugene Smith - Geometry - 1911 - 358 pages
...instructive one for a class, especially as the square can easily be made out of heavy pasteboard. THEOREM. **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. THEOREM. If from a point without a circle... | |
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