 | 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
...a square. 4. The opposite angles of an inscribed quadrilateral are supplementary. 5. If two chords intersect the prod'uct of the segments of one is equal to the product of the segments of the other. 6. Prove that if the radius be unity, the apothem of a regular inscribed decagon is iy/10 + 205. 7.... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...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... | |
 | George Albert Wentworth - Geometry - 1899 - 498 pages
...Then Zz? - AC* = 2 BC X MD. QE 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 O. To prove that OM X ON = OQ X OP. Proof. Draw MP and NQ.... | |
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...Then ~AB* - AC* = 2 BC X MD. QED 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 OH X ON= OQ X OP. Proof. Draw HP and NQ.... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...equivalent polygon. MISCELLANEOUS EXERCISES Ex. 1023. If two equal lines are divided externally so that the product of the segments of one is equal to the product of the segments of the other, the segments are equal respectively. * Ex. 1024. Two triangles are equal if the base, the opposite... | |
 | Universities and colleges - 1917 - 140 pages
...respectively, to the three sides of the other. 2. a) Prove: 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. b~) A and B are two points on a railway curve which is an arc of a circle. If the length of the chord... | |
 | Arthur Schultze - 1901 - 260 pages
...to the circles are equal. PROPOSITION XXXIII. THEOREM 312. 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. 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 in a circle, the product of the segments of one is equal to the product of the segments of the other. 
