Textbook of Engineering Drawing, Second Edition

4.12 Textbook of Enginnering Drawing-------------------

1. With 0 as centre, draw the given circle. P is any point on the circle at which tangent to
   be drawn (Fig 4.l6a)


2. Join 0 with P and produce it to pI so that OP = ppl


3. With 0 and pI as centres and a length greater than OP as radius, draw arcs intersecting
   each other at Q.


4. Draw a line through P and Q. This line is the required tangent that will be perpendicular
   to OP at P.
   (b) From any point outside the circle.


5. With 0 as centre, draw the given circle. P is the point outside the circle from which
   tangent is to be drawn to the circle (F ig 4 .16b).


6. Join 0 with P. With OP as diameter, draw a semi-circle intersecting the given circle at M.
   Then, the line drawn through P and M is the required tangent.


7. If the semi-circle is drawn on the other side, it will cut the given circle at MI. Then the
   line through P and MI will also be a tangent to the circle from P.

4.2 Conic Sections

Cone is formed when a right angled triangle with an apex and angle e is rotated about its altitude

as the axis. The length or height of the cone is equal to the altitude of the triangle and the radius of

the base of the cone is equal to the base of the triangle. The apex angle of the cone is 2 e
(Fig.4.20a).

When a cone is cut by a plane, the curve formed along the section is known as a conic. For this
purpose, the cone may be cut by different section planes (Fig.4.20b) and the conic sections obtained
are shown in Fig.4.20c, d, and e.

r

Apex

r

End

generator

rCutting plane

/ perpendicular

--+_;---4--_1. to the axis

Base

Circle

Fig.4.20a&b