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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. "
Elements of Plane Geometry - Page 179
by William Herschel Bruce, Claude Carr Cody (Jr.) - 1910 - 263 pages
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Harvard Examination Papers

Robert Fowler Leighton - 1880 - 428 pages
...parallelogram. Suggestion : Draw the diagonals of the quadrilateral. 6. If two chords intersect within the circle, the product of the segments of the one is equal to the product of the segments of the other. Prove. What does this proposition become when the chords are replaced by secants intersecting without...
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...291. 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. Let A~B and A'B' be any two chords of the circle ABB', passing through the point P. To prove that Ap^BP...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 414 pages
...the triangle ABC, or coincides with AE. Proposition 29. Theorem. 335. If two chords cut each other in a circle, the product of the segments of the one is...equal to the product of the segments of the other. Hyp. Let the chords AB, CD cut at P. To prove AP X BP = CP X DP. Proof. Join AD and BC. In the AS APD,...
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Report

Rutgers University. College of Agriculture - 1893 - 680 pages
...secant is measured by onehalf the difference of the intercepted arcs. 4. If two chords cut each other in a circle, the product of the segments of the one is...equal to the product of the segments of the other. 5. The area of a triangle is equal to half the product of its base and altitude. 6. The areas of si...
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An Examination Manual in Plane Geometry

George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...is equal to two right angles. 4. 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. 5. Two triangles having an angle of one equal to an angle of the other are to each other as the product...
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Plane Geometry

George D. Pettee - Geometry, Plane - 1896 - 272 pages
...any other and its external segment. Dem. AB x AD = AC x AE [= AF * ] PROPOSITION XXIII 220. Theorem. If two chords intersect within a circle, the product of the segments of one equals the product of the segments of the other. Dem. x = Y A=D &AEC DEB AE:CE=DE: BE AE x BE =...
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Essentials of Geometry (plane).

Webster Wells - Geometry - 1898 - 264 pages
...two chords be drawn through a fixed point within a circle, the product of the segments of one chord is equal to the product of the segments of the other. Given AB and A'B' any two chords passing through fixed point P within O AA'B. To Prove AP x BP = A'P x B'P....
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Plane and Solid Geometry

James Howard Gore - Geometry - 1898 - 232 pages
...229. If any tiuo 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. Let AB and A'B' be any two chords of the circle ABB' passing through the point P. To prove that Ap...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 498 pages
...PROPOSITION XXXII. THEOREM. 378. 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. Let any two chords MN and PQ intersect at O. To prove that OM X ON = OQ X OP. Proof. Draw MP and NQ....
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 424 pages
...two chords be drawn through a fixed point within a circle, the product of the segments of one chord is equal to the product of the segments of the other. Given AB and A'B' any two chords passing through fixed point P within O AA'B. To Prove AP x BP = A'P x B'P....
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