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" 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. "
Schultze and Sevenoak's Plane and Solid Geometry - Page 183
by Arthur Schultze, Frank Louis Sevenoak - 1913 - 457 pages
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Harvard Examination Papers

Robert Fowler Leighton - 1880 - 428 pages
...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 Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1890 - 420 pages
...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 - 682 pages
...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
...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. middle point of BC, prove that EF produced bisects AD. 8. Two similar triangles are to each other as...
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Plane Geometry

George D. Pettee - Geometry, Modern - 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 = CE...
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Plane and Solid Geometry

James Howard Gore - Geometry - 1898 - 232 pages
...to that side. PROPOSITION XVIII. THEOREM. 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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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

George Albert Wentworth - Geometry - 1899 - 500 pages
...first. Then AB* - AC* = 2 BC X MD. i,. E . D 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 0. To prove that OM X ON = OQ X OP. Proof. Draw MP and NQ....
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Plane Geometry

George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...first. Then Iff - AC* = 2 BC X MD. Q . E . D 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 0. To prove that OM X ON= OQ X OP. Proof. Draw HP 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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