Exercises in Geometry (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1909 edition. Excerpt: ... 12. Two chords are drawn from a point in a circumference to the ends of a diameter. If the chords are 3 and 4 inches long, what is the area of the circle? 13. The diameter of a circle is 11 feet. Find the diameter of a circle twice as large. 14. Find the side of a square which is equivalent to a circle of diameter 25. 15. Find the radius of a circle equivalent to a square whose side equals 6. 16. Find the area of a circle inscribed in a square containing 196 square feet. 17. Find the radius of a circle equivalent to an equilateral triangle whose side is 6. 18. If the apothem of a regular hexagon is 2, find the area of its circumscribed circle. Group VIII. Miscellaneous Theorems on Book V 1. The apothem of an inscribed equilateral triangle is equal to one half its radius. 2. The apothem of an inscribed regular hexagon is equal to one half the side of the inscribed equilateral triangle. 3. The radius of an inscribed regular polygon is a mean proportional between its apothem and the radius of the circumscribed regular polygon of the same number of sides. 4. The diagonals of a regular pentagon divide each other into extreme and mean ratio. 5. The square of the side of an inscribed equilateral triangle is equal to the sum of the square of a side of the inscribed square and the square of a side of the regular inscribed hexagon. 6. A square constructed on a diameter of a circle is equivalent to twice the area of the inscribed square. 7. If in a circle two chords intersect at right angles, and circles are constructed on the segments of the chords as diameters, the area of the given circle is equal to the sum of the areas of the four circles. 8. If on the legs of a right triangle as diameters, semicircles are described external to the triangle, and from...