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 148by Arthur Schultze - 1901Full view - About this book
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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 - 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... | |
| 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.... | |
| 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.... | |
| 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... | |
| |