 | Robert Fowler Leighton - 1880 - 428 σελίδες
...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 - 1890 - 420 σελίδες
...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 σελίδες
...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 - 1894 - 150 σελίδες
...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 - 1894 - 400 σελίδες
...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 - 1896 - 272 σελίδες
...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 - 1898 - 232 σελίδες
...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 - 1899 - 500 σελίδες
...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 - 1899 - 272 σελίδες
...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... | |
 | Arthur Schultze - 1901 - 260 σελίδες
...from any point in the perpendicular, AD, to the circles are equal. PROPOSITION XXXIII. THEOREM 312. If two chords intersect within a circle, the product...equal to the product of the segments of the other. Hyp. The chords AB and CD meet in E. To prove AE x EB = CE x ED. HINT. —What is the means of proving... | |
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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. 
