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" The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles. "
Elements of Plane and Solid Geometry - Page 221
by George Albert Wentworth - 1877 - 398 pages
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...Ex. 1308. The diagonals of a regular pentagon divide each other in extreme and mean ratio. Ex. 1309. The area of a regular inscribed hexagon is a mean...inscribed and circumscribed equilateral triangles. Ex. 1310. Any radius of a regular polygon bisects an angle of the polygon. Ex. 1311. The diagonals...
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Plane Geometry

Mabel Sykes, Clarence Elmer Comstock - Geometry, Modern - 1918 - 346 pages
...hexagon inscribed in the same circle. 4. Show that the area of a regular hexagon inscribed in a circle is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles. 5. The central angle of a regular octagon is 45°. 6. Given a side of a regular octagon, to construct...
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Plane Geometry: I. Abridged and Applied. II. College Preparatory

Matilda Auerbach, Charles Burton Walsh - Geometry, Plane - 1920 - 410 pages
...n-gon, and Atn that of a regular inscribed 2n-gon, fill out the accompanying table: Theoretic 1264. The area of a regular inscribed hexagon is a mean...inscribed and circumscribed equilateral triangles. d!255. An equilateral polygon circumscribed about a circle is regular if the number of its sides is...
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General Mathematics, Book 2

Raleigh Schorling, William David Reeve - Mathematics - 1922 - 476 pages
...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...inscribed and circumscribed equilateral triangles. 519. Extreme and mean ratio. In order to inscribe a regular decagon in a circle it is necessary to...
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Schultze and Sevenoak's Plane and Solid Geometry; Revised by Arthur Schultze

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...Ex. 1308. The diagonals of a regular pentagon divide each other in extreme and mean ratio. Ex. 1309. The area of a regular inscribed hexagon is a mean...inscribed and circumscribed equilateral triangles. Ex. 1311. The diagonals drawn from a vertex of a regular decagon divide that angle into eight equal...
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The Public-school Journal: Devoted to the Theory and Art of ..., Volume 12

Education - 1892 - 680 pages
...gauging, the cone is found to be filled only half its depth. How much does it lack of being full? (2) Show that the area of a regular inscribed hexagon...(%) of that of the regular circumscribed hexagon. — 0. F. Morgan. WATEBVILLE, Minn. 4. I would like a discussion of the following in THE JOUBNAL,:...
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Texas School Journal, Volume 24

Education - 1906
...to the altitude of another, what is the rati of their areas ? 7. The area of Ťan inscribed regular hexagon is a mean proportional between •the areas of the inscribed and circumscribed regular triangles. 8. With the vertices of a triangle as centers, describe three circles, each of which...
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A Class Book of Trigonometry

218 pages
...of a square described about the same circle. 7. The area of a regular octagon inscribed in a circle is a mean proportional between the areas of the inscribed and circumscribed squares of the same circle. 8. Each of three equal circles of radius a touches the other two ; find...
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