Week 2 – SS1 Second Term Technical Drawing Notes

 
 WEEK TWO DATE:………………
Escribed circles

 Content:
(i) Escribed circles.
(ii) Drawing of circles to touch some given points.

 Escribed circles.
Example 1 To escribe a circle on a given triangle.
    
Method:
(i) Draw the given triangle ABC.
(ii) Extend AC to D and AB to E.
(iii) Bisect the two exterior angles <DCB and <EBC
whose bisectors intersect at point O.
(vi) Draw a line from O perpendicular to any of the sides.
(v) With O as centre and radius OQ, escribe the circle.

 
 Example 2 To escribecircles on a given polygon.

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Method:
(i) Draw the given polygon and join opposite corners as shown above.
(ii) Bisect external angles P23 and S32 whose bisectors meet at point O, the centre of the circle.
(iii)Drop a perpendicular, OD to side 2-3. This is the radius of the circle.
(iv)With O as centre and radius OD, draw a circle. Repeat the above procedure for each side and circle.

 Evaluation Questions
1. Escribe a circle on a triangle of sides AB = 55mm, AC = 60mm and BC = 50mm.
2 . A regular hexagon has its sides 50mm long. Draw the hexagon and describe circles about it.

 
 
 
 Drawing of circles to pass through given points.

 Example 1To draw a circle to pass through a given point and touch a line at a given point

 
 
 
 
 
 
 
 
 Method:
(i) Locate the given point A and the given point R on the given line PQ.
(ii) Join the two given points ie, RA.
(iii)Erect a perpendicular at the point R on the given line.
(iv) Draw a line AO from point A to meet the perpendicular RS at point O; such that angle RAO is equal to
angle ORA. Point O is the centre of the circle that will pass through the given points.

 
 Example 2To draw a circle to pass through two given points and touch a given line.

 
 Method:
(i) Locate the two given points F and G and draw the
given line CD.
(ii) Draw a line to connect F and G and extend the line.
(iii) Extend the line CD to meet FG extended at point E.
(iv) Mark off EH equal to EG.
(v) Construct a semicircle on line FH.
(vi) Draw a line perpendicular to AH at point E to touch the semicircle at point K.
(vii) Mark off EP equal to EK.
(viii) Draw a line perpendicular to CD at point P and this line intersects the
bisector of FG at point O, thecentre of the circle required.
(ix) With O as centre and radius OP, draw the circle.

 
 Evaluation Questions

 
 
 
 
 
 
 1. Draw a line AB of length 80mm and locate a point Q on it which is 20mm from end B. Draw a circle to
touch points P which is at a suitably chosen distance and Q.

 
 
 2. Draw a circle to pass through points P and B and also touch line AC as shown below. Choose suitable
positions for points P and B and line AC.

 
 
 
 
     
 
 
 General evaluation/ revisional questions

1. Draw an equilateral triangle of side 60mm and inscribe three equal circles with two circles touching each side.
2. Choose any convenient point S and draw a tangent to the circle shown below.

    
    
    
    
    
    
    

3. Determine graphically the circumference of a circle, diameter 35mm.
4. Construct a line of approximate length to the given arc shown below.

 
 
 Reading assignment
Technical drawing by JN Green. Pages 21, 73-75.

 Weekend Assignment
Objective
1. Which of the following is correct in escribing a circle on a triangle? A. Bisect two internal angles.
B. Bisect two sides of the triangle. C. Bisect two external angles. D. Bisect three sides of the triangle.

 
 
 
 
 
 2. The radius of the circle drawn in the diagram above is represented by line A. CD. B. OB. C. OQ.
D. QD.
3. The figure below shows the construction of a/an A. circumscribed circle. B. circumscribed triangle.
C. escribed triangle. D. escribed circle.

 
 
 4. Which of the following is not a procedure for describing a circle round a polygon? A. Bisect two external
angles. B. Bisect two sides. C. Draw a line from the determined centre, parallel to one side.
D. Draw a line from the determined centre, perpendicular to one side.

 5.AB is the diameter of the circle shown below. What type of triangle is ABC? A. Scalene. B. Right
angled. C. Oblique. D. Isosceles.

 
 
 
 
 
 
 Theory
1 . A regular hexagon has its sides 50mm long. Draw the hexagon and describe circles about it.

 
 
 
 
 2. Draw a line AB of length 80mm and locate a point Q on it which is 20mm from end B. Draw a circle to
touch points P which is at a suitably chosen distance and Q.