366 GEOMETRY. 



tance B d, describe the arcfdg, cutting the chord 

 e B in f. Make dg equal to df; through g draw 

 g B, and it will be the tangent required. 



Prob. 12. Given three points, A, B, C. not in a 

 straight line, to describe a circle that shall pass 

 through them. 



Bisect the lines A B, B C, by the perpendicu- 

 lars a b, ba, meeting at d. Upon d, with the dis- 

 tance d A, </B, or dC, describe ABC, and it will 

 be the required circle. 



Prob. 13. To describe the segment of a circle, 

 of any length A B, and any height C D. 



Bisect AB by the perpendicular Dg> cutting 

 A B in c. From c make c D on the perpendicular 

 equal to C D. Draw A D, and bisect it by a per- 

 pendicular ef, cutting Dg in g. Upon g the ' 

 centre, describe A D B, and it will be the required 

 segment. 



Prob. 14. To describe the segment of a circle 

 by means of two rulers, to any length A B, and 

 perpendicular height C D in the middle of A B, 

 without making use of the centre. 



Place the rulers to the height at C ; bring the 

 edges close to A and B ; fix them together at C, 

 and put another piece across them to keep them 

 fast. Put in pins at A and B, then move the rulers 

 round these pins, holding a pencil at the angular 

 point C, which will describe the segment. 



Prob. 15. In any given triangle to inscribe a 

 circle. Bisect any two angles A and C, with the 

 lines A D and CDC. From D the point of inter- 

 section, let fall the perpendicular D E j it will be 

 the radius of the circle required. 



Prob. 16. In a given square, to describe a regu- 

 lar octagon. 



