^ New Method of drawing a Tangent to the Circle, [JaWi 



Article VIII. 



il new Method of drawing a Tangent to the Circle. 

 By Mr. William Ritchie, AM. of the Academy, Perth. 



(To the Editor of the Annals of Philosophy.) 

 SIR, 

 I HAVE taken the hberty of sending you a new method of 

 drawing a tangent to the circle which appears to me simpler 

 than any of those already known, and which I hope will find a 

 place in your Annals of Philosophy, For the advantage of the 

 young geometer, I have accompanied it with the analysis, or the 

 mode, by which it was discovered. I am, Sir, ^\ 



Your obedient servant, 



William Ritchie. 



Analysis, 



Let B F D be the given circle, C 

 its centre, and A the point, from which 

 the tangent is to be drawn ; and let 

 A F be the tangent required . Join C F, 

 -and produce it till F E be equal to 

 FC,join AE. 



Now since the angle AFE is equal 

 to A FC, each of them being a right 

 angle, and since F E is equal to F C, 

 and A F common to the two tri- 

 angles AFC and AFE, these tri- 

 angles are equal, and consequently A E is equal to A C, which 

 is given. Again C E is given, being equal to the diameter of 

 the circle ; therefore the point E is given, the Hne C E and F 

 its intersection with the circumference, which is the point 

 required. 



Composition. 



From A with the radius A C describe an arc, and from C with 

 at radius equal to the diameter of the circle describe another, 

 intersecting the former in E ; join C E and F its intersection 

 with the circumference of the circle will be the point of contact 

 required. 



For C E being equal to the diameter of the circle, and C F 

 the radius, F E is equal to F C, A C is equal to A E, and A F 

 common to the two triangles AFC and AFE; therefore, these 

 triangles are equal to each other, and consequently the angle 

 A F E is equal to the angle AFC; that is, A F C is a right 

 angle. Hence A F is a tangent to the circle. 



