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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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Elements of Geometry

George Washington Hull - Geometry - 1897 - 408 pages
...thirds of the area of the regular hexagon inscribed in the circle. 816. The area of an inscribed regular hexagon is a mean proportional between the areas of...inscribed and circumscribed equilateral triangles. 317. The square inscribed in a semicircle is equivalent to two fifths of the square inscribed in the...
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Plane and Solid Geometry

James Howard Gore - Geometry - 1898 - 232 pages
...inscribed hexagon = - V3. 3 3. Find the area of a square inscribed in a circle whose radius is 6. 4. Show that the area of a regular inscribed hexagon is a mean proportional between the areas of an inscribed, and of a circumscribed, equilateral triangle. PROPOSITION IX. THEOREM. 304. The area...
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Essentials of Geometry (plane).

Webster Wells - Geometry - 1898 - 282 pages
...(Prove, by aid of 164, that a O can be inscribed in FGHKL ; then use Ex. 7, p. 198.) E" - "D 25. The area of a regular inscribed hexagon is a mean proportional between the areas of an inscribed, and of a circumscribed equilateral triangle. (Prove, by aid of Exs. 8, 10, and 11, p....
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 450 pages
...pentagon. A (Prove, by aid of 164, that a O can be inscribed in FGHKL ; then use Ex. 7, p. 198.) 25. The area of a regular inscribed hexagon is a mean proportional between the areas of an inscribed, and of a circumscribed equilateral triangle. (Prove, by aid of Exs. 8, 10, and 11, p....
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New Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 416 pages
...circumference in C, D ; draw CD, DB, BC, and prove A BCD equilateral. 444. The area of an inscribed regular hexagon is a mean proportional between the areas of...inscribed and circumscribed equilateral triangles. 445. Show how, with compasses alone, to divide a circumference into six equal arcs. 446. Prove that...
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The Elements of Plane Geometry

Charles Austin Hobbs - Geometry, Plane - 1899 - 240 pages
...equal to one half the area of the inscribed regular hexagon. Ex. 659. The area of an inscribed regular hexagon is a mean proportional between the areas of...inscribed and circumscribed equilateral triangles. Proposition 217. Theorem. 254. The area of a circle is equal to one half the product of its circumference...
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 424 pages
...pentagon. (Prove, by aid of 164, that a 0 can be inscribed in FGHKL ; then use Ex. 7, p. 198.) E" "D 25. The area of a regular inscribed hexagon is a mean proportional between the areas of an inscribed, and of a circumscribed equilateral triangle. (Prove, by aid of Exs. 8, 10, and 11, p....
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New Plane Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry, Modern - 1899 - 272 pages
...circumference in C, D; draw CD, DB, BC, and prove A BCD equilateral. 444. The area of an inscribed regular hexagon is a mean proportional between the areas of...inscribed and circumscribed equilateral triangles. 445. Show how, with compasses alone, to divide a circumference into six equal arcs. 446. Prove that...
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Plane and Solid Geometry

James Howard Gore - Geometry - 1899 - 266 pages
...the perimeter and area of a regular pentagon whose apothem is 8. 4. The area of an inscribed regular hexagon is a mean proportional between the areas of the inscribed and the circumscribed equilateral triangles. 5. The area of an inscribed regular octagon is equal to that...
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Plane Geometry

Arthur Schultze - 1901 - 260 pages
...Ex. 940. The diagonals of a regular pentagon divide each other into extreme and mean ratio. Ex. 941. The area of a regular inscribed hexagon is a mean...inscribed and circumscribed equilateral triangles. Ex. 942. Any radius of a regular polygon bisects an angle of the polygon. Ex. 943. The diagonals drawn...
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