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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

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....
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Plane and Solid Geometry

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....
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Geometry: Plane Trigonometry. Chain Surveying. Compass Surveying. Transit ...

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...
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Plane and Solid Geometry

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...
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Wentworth's Plane Geometry

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...
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Elements of Plane Geometry

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...
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Elements of Plane Geometry

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...
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College Entrance Examination Papers in Plane Geometry

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...
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Secondary-school Mathematics, Book 2

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...
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The Teaching of Geometry

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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