 The area of a regular hexagon inscribed in a circle is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.  Elements of Geometry - Page 248by Andrew Wheeler Phillips, Irving Fisher - 1896Full view - About this book
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...part of the diameter drawn through the opposite angle. 17. The area of an inscribed regular hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles. 18. The square of the side of an equilateral triangle inscribed in a circle... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...pentagon divide each other into extreme and mean ratio. Ex. 941. The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles. Ex. 942. Any radius of a regular polygon bisects an angle of the polygon. Ex.... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...pentagon divide each other into extreme and mean ratio. Ex. 941. The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles. Ex. 942. Any radius of a regular polygon bisects an angle of the polygon. Ex.... | |
 | James McMahon - Geometry, Plane - 1903 - 380 pages
...such that the perpendiculars to it from three given points may have given ratios to each other. 3. A regular polygon inscribed in a circle is a mean proportional between the inscribed and circumscribed circles of half the number of sides. 4. Construct a triangle, being given... | |
 | Daniel Alexander Murray - 1906 - 466 pages
...that the area of the triangle is equal to the square of half the base. 15. (a) Show that the area of a regular polygon inscribed in a circle is a mean proportional between the areas of an inscribed and circumscribing polygon of half the number of sides. (6) The sides of a triangle are... | |
 | Daniel Alexander Murray - Plane trigonometry - 1908 - 358 pages
...that the area of the triangle is equal to the square of half the base. 15. (a) Show that the area of a regular polygon inscribed in a circle is a mean proportional between the areas of an inscribed and circumscribing polygon of half the number of sides. (6) The sides of a triangle are... | |
 | Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...another hexagon. Compare the areas of the two hexagons. 23. The area of an inscribed regular hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles. 24. Join the alternate vertices of any regular polygon and show that a similar... | |
 | Daniel Alexander Murray - Plane trigonometry - 1911 - 158 pages
...Prove r=— ""— . Write two similar formulas coS2" involving b, c. 9. (a) Show that the area of a regular polygon inscribed in a circle is a mean proportional between the areas of an inscribed and circumscribing polygon of half the number of Bides, (b) The sides of a triangle are... | |
 | Geometry, Plane - 1911 - 192 pages
...without it. 6. Prove that the area of any regular polygon of an even number of sides (2ri) inscribed jn 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... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...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 divide that... | |
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