 | Edward Olney - Geometry - 1872 - 472 pages
...LINES INTERSECTING EACH OTHER, AND INTERSECTED BY A CIRCUMFERENCE. PROPOSITION I. 355. TJieorem. — If two chords intersect each other in a circle, their...other. DEM. — Let the chords AC and BD intersect at O ; then is AO : BO : : DO : CO, whence AO x CO = BO x DO. For, draw AD and BC. The two triangles AOD... | |
 | Edward Olney - Geometry - 1877 - 272 pages
...LINES INTERSECTING EACH OTHER, AND INTERSECTED BY A CIRCUMFERENCE. PROPOSITION I. 355. Tlteorem.—If two chords intersect each other in a circle, their...chord equals the product of the segments of the other. DEM.—Let the chords AC and BD intersect at O; then is AO : BO :: DO : CO, whence AO x CO = BO x DO.... | |
 | Edward Olney - Geometry - 1879 - 502 pages
...THE SEGMENTS OF TWO LINES INTERSECTING EACH OTHER, AND INTERSECTED BT A CIRCUMFERENCE. PROPOSITION L 355. Theorem. — If two chords intersect each other...equiangular, and hence similar ; since the angles at 0 are vertical, and consequently equal (134), and D = C, became b.>ih are measured by | arc AB (21O).... | |
 | Edward Olney - 1879 - 278 pages
...elementary properties of plane figures, which we are able to discover by means of this doctrine. OP THE RELATIONS OF THE SEGMENTS OF TWO LINES INTERSECTING...other. DEM. — Let the chords AC and BD intersect at O ; then is AO : BO : : DO : CO, whence AO x CO = BO x DO. For, draw AD and BC. The two triangles AOD... | |
 | Edward Olney - Geometry - 1883 - 352 pages
...LINES INTERSECTING EACH OTHER, AND INTERSECTED BY A CIRCUMFERENCE. PROPOSITION I. 402. Theorem. — // two chords intersect each other in a circle, their...chord equals the product of the segments of the other. DEMONSTRATION. Let the chords AC and BD (Fig. 203) intersect at 0. OB OC We are to prove that OA =... | |
 | Joe Garner Estill - 1896 - 186 pages
...through the middle point of the base. 3. If two chords be drawn through a fixed point within a circle, the product of the segments of one chord equals the product of the segments of the other. 4. The radius of a circle is 10 ; inscribe within it a regular decagon and compute the length of its... | |
 | Joe Garner Estill - 1896 - 214 pages
...through the middle point of the base. 3. If two chords be drawn through a fixed point within a circle, the product of the segments of one chord equals the product of the segments of the other. 4. The radius of a circle is 10 ; inscribe within it a regular decagon and compute the length of its... | |
 | Frank Charles Touton - Geometry, Plane - 1924 - 134 pages
...of the examiners to measure the knowledge of the theorem: "If two chords intersect within a circle, the product of the segments of one chord equals the product of the segments of the other." Now this general theorem is used by but 46.0 per cent of the pupils. Had the exercise read: "Find first... | |
 | Frank Charles Touton - Geometry, Plane - 1924 - 136 pages
...of shorter chord only. (10) Theorem used: If two chords are drawn through a point within a circle, the product of the segments of one chord equals the product of the segments of other. (11) Absurd error or statement without any apparent reason. (12) Method not evident. (13) Distance... | |
| |
If two chords intersect each other in a circle, their segments are reciprocally proportional ; whence the product of the segments of one chord equals the product of the segments of the other. 