 If two chords intersect within a circle, the product of the segments of the one is equal to the product of the segments of the other.  Plane Geometry - Page 192by Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - 1920 - 305 pagesFull view - About this book
 | George D. Pettee - Geometry, Modern - 1896 - 272 pages
...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 x DE PKOPOSITION XXIV 221. Theorem. The product of... | |
 | John Alton Avery - Geometry, Modern - 1903 - 136 pages
...draw tangent AC, and secant AY intersecting circumference at X and Y. Draw CX and CY. THEOREM XIV 177. If two chords of a circle intersect, the product of...one equals the product of the segments of the other. Hyp. In O ADBC, let chords AB and CD intersect at X. To prove that AX x XB = CX x XD. SUG. 1. Draw... | |
 | Levi Leonard Conant - Geometry - 1905 - 154 pages
...D, E ; prove that the chord DE is parallel to the tangent at C. 149. Two finite lines meet so that the product of the segments of one equals the product of the segments of the . other ; prove that the four extremities of the two lines are concyclic. 150. ABC is a triangle right angled... | |
 | Webster Wells - Geometry, Plane - 1908 - 208 pages
...altitudes to the equal sides of an isosceles triangle intersect in a point such that the product of segments of one equals the product of the segments of the other. Ex. 23. The diagonals of inscribed quadrilateral ABCD intersect at O. If OM and OS are the altitudes... | |
 | Webster Wells - Geometry - 1908 - 329 pages
...altitudes to the equal sides of an isosceles triangle intersect in a point such that the product of segments of one equals the product of the segments of the other. Ex. 23. The diagonals of inscribed quadrilateral AS CD intersect at. 0. If OR and OS are the altitudes... | |
 | Webster Wells - Geometry - 1908 - 336 pages
...altitudes to the equal sides of an isosceles triangle intersect in a point such that the product of segments of one equals the product of the segments of the other. Ex. 23. The diagonals of inscribed quadrilateral ABCD intersect at O. If OK and OS are the altitudes... | |
 | Charles E. Larard, Henry A. Golding - Engineering - 1909 - 556 pages
...corresponding sides or lines in the two figures, taken two and two, are proportional. Euclid proves that if two chords of a circle intersect, the product of the segments of one of them is equal to the product of the segments of the other. Hence, if AC, BD (fig. 1 IA) be two intersecting... | |
 | Correspondence schools and courses - 1909 - 870 pages
...described from the FIG. 74 Fio. 75 same center, as in Fig. 75, they are called concentric circles. 79. If two chords of a circle intersect, the product of the segments (parts) thus formed of one of the chords is equal it Pro. 7« to the product of the segments of the... | |
 | George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...* 299. If two chords intersect within a circle, the product of the segments of the one is equal to the product of the segments of the other. Given the chords AB and CD, intersecting at P. To prove that PAxPB=PCx PD. Proof. Draw AC and BD. Then since Z a = Z a', § 214 (Each is measured... | |
 | Geometry, Plane - 1911 - 192 pages
...SEPTEMBER, 1908 1. The sum of the three interior angles of a triangle is equal to two right angles. 2. If two chords of a circle intersect, the product of the segments of the one is equal to the product of the segments of the other. 4. The diameter AB of a circle is trisected... | |
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