| 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, CPB,... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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.... | |
| 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.... | |
| Arthur Schultze - 1901 - 260 pages
...WC2. * Ex. 631. Conversely, if, in the same diagram, D be taken so that 01? - CFD 2 = Off - (FC 2 , **then the tangents drawn from any point in the perpendicular,...equal to the product of the segments of the other.** D Hyp. The chords AB and CD meet in E. To prove AE x EB = CE x ED. HINT. — What is the means of proving... | |
| Alan Sanders - Geometry, Modern - 1901 - 260 pages
...contact into segments whose product is equal to the square of the radius. PROPOSITION XXII. THEOREM 528. **If two chords intersect within a circle, the product...equal to the product of the segments of the other.** Let the chords AB and CD intersect at E. To Prove AE . ER = CE • ED. Proof. Draw AC and DB. Prove... | |
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