 Prove that the area of an inscribed regular hexagon is a mean proportional between the areas of the inscribed and the circumscribed equilateral triangles.  Plane Geometry - Page 243by Edward Rutledge Robbins - 1906 - 254 pagesFull view - About this book
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 488 pages
...regular pentagon divide each other in extreme and mean ratio. Ex. 1309. The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles. * Ex. 1311. The diagonals drawn from a vertex of a regular decagon... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...regular pentagon divide each other in extreme and mean ratio. Ex. 1309. The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles. Ex. 1311. The diagonals drawn from a vertex of a regular decagon... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1915 - 280 pages
...The area of the inscribed equilateral triangle. (/) The area of the inscribed regular hexagon. (g) The area of the inscribed regular octagon. (A) The...equilateral triangle, and C is the midpoint of AB. If AB is prolonged to O making BO equal to BC, and OT is drawn tangent to the circle at T, OT is f the radius.... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1915 - 282 pages
...triangle. (/) The area of the inscribed regular hexagon. (g) The area of the inscribed regular octagon. (h) The area of the circumscribed regular hexagon. 63....equilateral triangle, and C is the midpoint of AB, If AB is prolonged to O making BO equal to BC, and OT is drawn tangent to the circle at T, OT is f the radius.... | |
 | John Charles Stone, James Franklin Millis - Geometry - 1916 - 298 pages
...18. The area of an inscribed regular hexagon. 19. The area of a circumscribed regular hexagon. 20. The area of an inscribed regular hexagon is a mean...proportional between the areas of the inscribed and circumscribed equilateral triangles. 21. If the diagonals joining the alternate vertices of a regular... | |
 | William Betz - Geometry - 1916 - 536 pages
...area of the circumscribed equilateral triangle. 9. The area of the regular inscribed hexagon is the mean proportional between the areas of the inscribed and the circumscribed equilateral triangles. 10. In Ex. 6 compare the area of the given hexagon with that of any one of the figures pointed out.... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...regular pentagon divide each other in extreme and mean ratio. Ex. 1309. The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles. Ex. 1310. Any radius of a regular polygon bisects an angle of... | |
 | Matilda Auerbach, Charles Burton Walsh - Geometry, Plane - 1920 - 410 pages
...5. Prove that the area of any regular polygon of an even number of sides (2n) inscribed in a circle is a mean proportional between the areas of the inscribed and the circumscribed polygons of half the number of sides. If n be indefinitely increased, what limit or limits do these... | |
 | Raleigh Schorling, William David Reeve - Mathematics - 1922 - 476 pages
...inscribed octagon is r V 2 — V2, that its apothem is ^ V 2 — A/2, and that its area is 2r'V2. '" 14 . The area of an inscribed regular hexagon is a mean...proportional between the areas of the inscribed and circumscribed equilateral triangles. 519. Extreme and mean ratio. In order to inscribe a regular decagon... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...regular pentagon divide each other in extreme and mean ratio. Ex. 1309. The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles. Ex. 1311. The diagonals drawn from a vertex of a regular decagon... | |
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