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" 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. "
Plane Geometry - Page 148
by Arthur Schultze - 1901
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Questions Set at the Examinations

Universities and colleges - 1917 - 140 pages
...congruent if the three sides of one are equal, respectively, to the three sides of the other. 2. a) Prove: If two chords intersect within a circle, the product...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...
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Elements of Plane Geometry

Alan Sanders - Geometry, Modern - 1901 - 260 pages
...into segments whose product is equal to the square of the radius. PROPOSITION XXII. THEOREM 528. // 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 . EB = CE . ED. Proof. Draw AC and DB. Prove A...
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Plane and Solid Geometry

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...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 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...
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Plane and Solid Geometry

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...
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Some Noteworthy Properties of the Triangle and Its Circles

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...
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Elements of Plane and Solid Geometry

Alan Sanders - Geometry - 1903 - 392 pages
...into segments whose product is equal to the square of the radius. 162 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 • EB = CK • ED. Proof. Draw AC and DB. Prove...
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Elements of Plane and Solid Geometry

Alan Sanders - Geometry - 1903 - 396 pages
...product is equal to the square of the radius. [Show that OAB is a RAA] PROPOSITION XXII. THEOREM 528. //' two chords intersect within a circle, the product...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....
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1904 - 496 pages
...first. Then Zz? ' -~AC* = 2BC X MD. VQED 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 ON X ON = OQ X OP. Proof. Draw HP and NQ....
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Annual report (Ohio. State Medical Board). 1904

1904 - 60 pages
...straight line into five equal parts. 4. If two cords intersect within a circle prove that the products of the segments of one is equal to the product of the segments of the other. 5. Show how to construct a square equivalent to the difference of two given squares. 6. Show how to...
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