Original Exercises in Plane and Solid Geometry (Paperback)

Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book: III. CONSTRUCTIONS Construct a circle with its center in a given line which shall be: ? 301. Tangent at a given point to another given line. 302. Tangent to two other given lines. 303. Tangent at a given point to a given circle. When is the center of the required circle infinitely distant ? Construct a circle with its center on a given circle which shall be: ? 30. Tangent to two given lines. 305. Tangent to a given circle at a given point. 306. Tangent to a given line at a given point. 307. Construct a circle which shall be tangent to a given line, and to a given circle at a given point. 308. Construct a circle which shall be tangent to a given circle, and to a given line at a given point. 309. Construct a triangle, having given the vertex, the orthocenter, and the center of the circumscribed circle. Hint. Bisect that part of the altitude drawn from the given vertex, which lies between the orthocenter and the circumference of the circumscribed circle. Construct a circle of given radius r, which shall: ? 310. Pass through a given point and be tangent to a given line. 311. Pass through a given point and be tangent to a given circle. 312. Pass through a given point and cut a given circle in a diameter. 313. Pass through a given point and cut a given circle orthogonally. Hint. Remember that at any given point on the circle the direction of the circle and the direction of the tangent at that point are the same. 314. Be tangent to a given line and to a given circle. 315. Be tangent to two given circles. 316. Be tangent to a given circle and cut another given circle orthogonally. 317. Be tangent to a given line and cut a given circle orthogonally. 318. Be tangent to a given line and cut a given circle in a diameter....