 | 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... | |
 | 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,... | |
 | Rutgers University. College of Agriculture - 1893 - 680 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... | |
 | 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... | |
 | Webster Wells - Geometry - 1894 - 400 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. Let AJl and A'B' be any two chords passing through the fixed point P within the circle ABB'. To prove APxBP^A'PXB'P.... | |
 | George D. Pettee - Geometry, Modern - 1896 - 272 pages
...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... | |
 | 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 x Bp... | |
 | 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. Z... | |
 | 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. Z a... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...is divided at the point of contact into segments whose product is equal to the square of the radius. PROPOSITION XXII. THEOREM 528. // two chords intersect...mutually equiangular and therefore similar. Whence AE_^KD CE EB .-. AE . EB = CE . ED. (?) QED CONVERSELY. If two lines AB and CD intersect at E, so that... | |
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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. 
