Plane Geometry, with Problems and Application

Plane Geometry, with Problems and Application

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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. 1918 edition. Excerpt: ...does he move? SUPPLEMENTARY PROBLEMS SEGMENT OF A CIRCLE CONTAINING A GIVEN ANGLE 287. Problem. On a given line as a chord to construct a segment of a circle which shall contain a given inscribed angle. Given a line AB and an angle such as Z 1. To construct on AB as a chord a segment of a Q which shall contain an inscribed Z equal to Z 1. Construction and Proof: Through B draw X Y so as to make Z ABX =Z1. At B erect BK _L IT, and at C, the. middle point of AB, erect CL _L AB. Then BK and CL meet at 0, equidistant from A and B. 154, 191 With O as a center and OB as a radius draw a Q. Let Z P be any angle inscribed in the segment AMB. Then, measure ZP = ANB and measure Z ABX = ANB..-.Z P=Z ABX= Zl.. Q. E. F. Pages 150-151 may be omitted without destroying the continuity. CONSTRUCTING COMMON TANGENTS TO TWO CIRCLES 288. Problem. To draw a common tangent to two circles neither of which lies wholly inside the other. Given (c) O and O' such that the radius of the first is the greater. Required to draw a tangent common to both circles. Construction. Draw an auxiliary circle with center O and radius equal to the difference of the two given radii in figure 1 and equal to the sum of these radii in figure 2. In each case draw a tangent O'D to this auxiliary circle. Draw the radius OD, thus fixing the point P. Draw O'P II DP, thus fixing the point P. Then PP is the required tangent. Outline of Proof: Show that, in each case, PPO'D is a rectangle, thus making PP perpendicular to the radii OP and O'P, that is, tangent to each circle. 289. Definition. A common tangent to two circles is called direct if it does not cross the line-segment connecting the centers, and transverse if it does cross this segment. Thus, PP: is a direct tangent in Fig. 1, .show more

Product details

  • Paperback | 64 pages
  • 189 x 246 x 3mm | 132g
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236605020
  • 9781236605023