Geometrical construction and Projection System

Geometric Construction:
15. To draw an arc of given radius to touch two circles one from outside and the other from inside:
1. Assume that the radii of the given circles are 15 and 25 mm, spaced 60 mm apart, and that the radius of arc to touch them is 75 mm.
2. From centre of circle A draw an arc equal to 75 - 25 = 50 mm.
3. From centre of circle B draw an arc equal to 75+ 15 = 90 mm.
4. The above arcs intersect at point O. Draw from this origin point a straight line to the centre of circle B which intersect with the circumference of this circle at point C2 and another line from O to the centre of circle A and its extension will intersect with circumference of circle A at point C1.
5. With a radius of 75 mm, draw an arc from point O, reaching points of tangency C1 and C2. This will be the arc touching two circles one from outside and the other from inside.

16. To construct a regular Octagon :( diameter of circle known)
Assume radius (r) = 60 mm
1. Draw orthogonal lines with an angle 90o which represent centre lines of the circle.
2. From the origin point (o) draw a circle using known radius.
3. As showing in figure below using Tee-square and 45o set-square ( 45o triangle) draw (8) tangential lines to the circle.
4. From intersecting points for the tangential lines through the circumference of the circle join AB,BC,CD,DE,EF,FG,GH and HA to get the required Octagon.