 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
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...area of the circumscribed regular hexagon. Ex. 458. The area of an inscribed regular hexagon is the mean proportional between the areas of the inscribed and the circumscribed equilateral triangles. Ex. 459. The square of the side of an inscribed equilateral triangle is equal to three times the square... | |
 | George Albert Wentworth - Geometry - 1899 - 498 pages
...area of the circumscribed regular hexagon. Ex. 458. The area of an inscribed regular hexagon is the mean proportional between the areas of the inscribed and the circumscribed equilateral triangles. Ex. 459. The square of the side of an inscribed equilateral triangle is equal to three times the square... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...each of its sides will cut off one-fourth 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... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...concentric circles the radii of which are a and & respectively. 5. The area of a regular inscribed hexagon is a mean proportional between the areas of...inscribed and the circumscribed equilateral triangles. [See Ex. to Prop. 6.] 6. The diagonals joining the alternate vertices of a regular hexagon form by... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...regular 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... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...regular 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... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...regular 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... | |
 | Arthur Schultze - 1901 - 260 pages
...regular 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... | |
 | Alan Sanders - Geometry - 1903 - 396 pages
...concentric circles the radii of which are a and b respectively. 5. The area of a regular inscribed hexagon is a mean proportional between the areas of...inscribed and the circumscribed equilateral triangles. [See Ex. to Prop. 0.] 6. The diagonals joining the alternate vertices of a regular hexagon form by... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...area of the circumscribed regular hexagon. Ex. 458. The area of an inscribed regular hexagon is the mean proportional between the areas of the inscribed and the circumscribed equilateral triangles. Ex. 459. The square of the side of an inscribed equilateral triangle is equal to three times the square... | |
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