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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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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 393 pages
...regular inscribed hexagon is twice the area of the inscribed equilateral triangle. 4. The area of the regular inscribed hexagon is threefourths of that of the regular circumscribed hexagon. 5. The area of the regular inscribed hexagon is a mean proportional between the areas of the inscribed...
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Elementary Trigonometry

John Maximilian Dyer - Plane trigonometry - 1891 - 306 pages
...in its construction (Eue. IV. 11) ::,/5:1(8) The area of the regular hexagon inscribed in a circle is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles, (9) One circle is inscribed in and another is circumscribed about a regular polygon of и sides. If...
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Elementary Geometry

William Chauvenet - 1893 - 340 pages
...regular inscribed triangle is one-half the area of the regular inscribed hexagon. 6. The area of the regular inscribed hexagon is three-fourths of that of the regular circumscribed hexagon. 7. The area of the regular inscribed hexagon is a mean proportional between the areas of the inscribed...
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 320 pages
...apothems, their radii, or their sides. Proved with cor. 1. EXERCISES. 470. The area of an inscribed regular hexagon is a mean proportional between the areas of...inscribed and circumscribed equilateral triangles. 471. Show how, with compasses alone, to divide a circumference into six equal arcs. 472. Prove that...
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Elements of Geometry: Plane and Solid

John Macnie - Geometry - 1895 - 392 pages
...equilateral triangle is to the radius of the circumscribing circle as 3 is to 2. 614. The area of the regular hexagon is a mean proportional between the areas of...inscribed and circumscribed equilateral triangles. 615. The square of a side of an inscribed equilateral triangle is equivalent to three times the square...
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 320 pages
...apothems, their radii, or their sides. Proved with cor. 1. EXERCISES. 470. The area of an inscribed regular hexagon is a mean proportional between the areas of...inscribed and circumscribed equilateral triangles. 471. Show how, with compasses alone, to divide a circumference into six equal arcs. 472. Prove that...
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Plane Geometry

George D. Pettee - Geometry, Plane - 1896 - 272 pages
...whose diameter is a chord of the outer circle, tangent to the inner circle. 396. The area of a regular hexagon is a mean proportional between the areas of...inscribed and circumscribed equilateral triangles. MAXIMA AND MINIMA 289. Definitions. Of magnitudes of the same kind, that which is greatest is a maximum;...
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Exercises in Wentworth's Geometry: With Solutions

George Albert Wentworth - Geometry - 1896 - 296 pages
...inscribed hexagon — J-RVS (Ex. 380). But TEACHERS EDITION. Ex. 392. The area of an inscribed regular hexagon is a mean proportional between the areas of...inscribed and circumscribed equilateral triangles. PROOF. Area of inscribed equilateral A whose sido is a = |xf R = ^~ x ^ - JR^Vs. (Ex.378) Area of circumscribed...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 556 pages
...triangles be circumscribed about and inscribed in a given triangle, the area of the given triangle is a mean proportional between the areas of the inscribed and circumscribed triangles. 105. Any fourth point P is taken on the circumference of a circle through A, B, and C. Prove...
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Elements of Geometry, Volume 1

Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...of those which fall upon the other side. 128. The area of any regular polygon inscribed in a circle is a mean proportional between the areas of the inscribed and circumscribed polygons of half the number of sides. 129. If, on the sides of a right triangle as diameters, semi-circumferences...
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