 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.  Plane Geometry - Page 166by George Albert Wentworth - 1899 - 256 pagesFull view - About this book
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...is equal to the square of the radius. PROPOSITION XXII. THEOREM 528. // two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other. Let the chords AB and CD intersect at E. To Prove AE . EB = CE . ED. Proof. Draw AC and DB. Prove A AEC... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...perpendicular, AD, 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... | |
 | Universities and colleges - 1917 - 140 pages
...are equal, 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, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...perpendicular, AD, 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... | |
 | Arthur Schultze - 1901 - 260 pages
...perpendicular, AD, 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... | |
 | Arthur Schultze - 1901 - 260 pages
...and extremes of the resulting proportion. Ex. 585. If two chords intersect within a circumference, the product of the segments of one is equal to the product of the segments of the other. Ex. 586. If from any point E in the chord AB the perpendicular EC be drawn upon the diameter AD, then... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...and extremes of the resulting proportion. Ex. 585. If two chords intersect within a circumference, the product of the segments of one is equal to the product of tlje segments of the other. Ex. 586. If from any point E in the chord AB the perpendicular EC be drawn... | |
 | William Herschel Bruce - Triangle - 1902 - 38 pages
...Fig- 313. Any two altitudes of a triangle cut each other so that the product of the segments of the one is equal to the product of the segments of the other. Proof. By 11, A, B, D, E (Fig. 2), are concyclic. (If two chords of a O intersect, the product of the... | |
 | Alan Sanders - Geometry - 1903 - 396 pages
...the radius. [Show that OAB is a RAA] PROPOSITION XXII. THEOREM 528. //' two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other. Let the chords A Lt and ct) intersect at E. To Prove AK • EB = CE • ED. Proof. Draw AC and DB. Prove... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...AC* = 2 KM* + 2 AM*. Subtract the second equality from the first. Then Zz? ' -~AC* = 2BC X MD. VQED PROPOSITION XXXII. THEOREM. 378. If two chords intersect...the other. Let any two chords MN and PQ intersect at O. To prove that ON X ON = OQ X OP. Proof. Draw HP and NQ. Z a = Z a', § 289 (each being measured... | |
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