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**Engineering Graphics Circles, Semi Circles**

**2.1 INTRODUCTION**

As we know that wheel has been the most revolutionary invention for transport and industrial revolution. In engineering many machine parts are circular in shape or uses part of a circle or some of their features. e.g. gears, pulleys, bearings etc. We shall be required to construct circle and circular features in many drawings of Engineering Graphics. In this chapter let us learn how to draw these and acquire the skill very well.

**2.2 LET US RECALL**

You have already learnt about circle and its construction in variety of problems in your earlier classes. Let us recall. Study the figure 2.1 and fill in the blanks with the choices given : (point of contact, Centre, Radius, Diameter, Chord, Tangent, Normal, Sector, ∠OPG|∠OPF, segments, O, OA, OC, OP, OB, radii, BC, P, arc, DE, twice, Semi circle.)

Q1. The fixed point ....... is the ...............

Q2. The constant distance from centre to any point on its circumference distances ........, ............ , ............. and ................ are .................

Q3. The line passing through the centre having its extremities on the circumference of the circle is ................. and is called ................

Q4. The line touching the circle at a point ....................... is known as ........................... .

Q5. The line perpendicular to tangent and joining the centre is named ..................... and angles ............... and ................... are 90°.

Q6. One of the ...................... is AC.

Q7. The portion of circle with arc BP and two corresponding radii is named................ .

Q8. The line segment ................ is known as .............................

Q9. The chord divides the circle in two parts called .................. .

Q10. The diameter is ................................ the radius.

Q11. A circle can be drawn when its ........................ and ................................... are given.

Q12. A diameter divides the circle into to equal halves which are known as ...................... .

Q13. The point P is named .....................

**2.3 CONSTRUCTIONS OF CIRCLES**

**SOLVED EXAMPLES**

**Example 1**

To find the centre of a given circle which is drawn without using compass. Use any circular object like glass tumbler, bottle cap etc. Solution : Refer Fig. 2.2 (i) Draw AB and CD two chords of the circle at any angle (except parallel chords) (ii) Find the perpendicular bisectors of both of them (iii) The point of intersection of the right bisectors (point O) is the centre of the circle.

**Example 2**

To draw a circle passing through three non-collinear points A, B and C. Solution : Refer fig. 2.3 (i) Take any three points A, B, and C. (ii) Join A with B and B with C. (iii) Find the perpendicular bisectors of AB and BC. (iv) Name the point of intersection of these perpendicular bisectors as O. (v)Now with O as centre and OA or OB or OC as radius, draw the circle through A, B and C points.

**Example 3**

Given the arc PQ, complete the circle.

Solution : Refer Fig. 2.4 Take any circular arc PQ (ii) Take any point R on PQ (iii) Find the perpendicular bisectors of PR and RQ (iv) Name the point of intersection of these as O. (v) Now draw a circle with O as centre and OP as radius. Can you name the other two radii like OP ?

You have already learnt about circle and its construction in variety of problems in your earlier classes. Let us recall. Study the figure 2.1 and fill in the blanks with the choices given : (point of contact, Centre, Radius, Diameter, Chord, Tangent, Normal, Sector, ∠OPG|∠OPF, segments, O, OA, OC, OP, OB, radii, BC, P, arc, DE, twice, Semi circle.)

Q1. The fixed point ....... is the ...............

Q2. The constant distance from centre to any point on its circumference distances ........, ............ , ............. and ................ are .................

Q3. The line passing through the centre having its extremities on the circumference of the circle is ................. and is called ................

Q4. The line touching the circle at a point ....................... is known as ........................... .

Q5. The line perpendicular to tangent and joining the centre is named ..................... and angles ............... and ................... are 90°.

Q6. One of the ...................... is AC.

Q7. The portion of circle with arc BP and two corresponding radii is named................ .

Q8. The line segment ................ is known as .............................

Q9. The chord divides the circle in two parts called .................. .

Q10. The diameter is ................................ the radius.

Q11. A circle can be drawn when its ........................ and ................................... are given.

Q12. A diameter divides the circle into to equal halves which are known as ...................... .

Q13. The point P is named .....................

**2.3 CONSTRUCTIONS OF CIRCLES**

**SOLVED EXAMPLES**

**Example 1**

To find the centre of a given circle which is drawn without using compass. Use any circular object like glass tumbler, bottle cap etc. Solution : Refer Fig. 2.2 (i) Draw AB and CD two chords of the circle at any angle (except parallel chords) (ii) Find the perpendicular bisectors of both of them (iii) The point of intersection of the right bisectors (point O) is the centre of the circle.

**Example 2**

To draw a circle passing through three non-collinear points A, B and C. Solution : Refer fig. 2.3 (i) Take any three points A, B, and C. (ii) Join A with B and B with C. (iii) Find the perpendicular bisectors of AB and BC. (iv) Name the point of intersection of these perpendicular bisectors as O. (v)Now with O as centre and OA or OB or OC as radius, draw the circle through A, B and C points.

**Example 3**

Given the arc PQ, complete the circle. Solution : Refer Fig. 2.4 Take any circular arc PQ (ii) Take any point R on PQ (iii) Find the perpendicular bisectors of PR and RQ (iv) Name the point of intersection of these as O. (v) Now draw a circle with O as centre and OP as radius. Can you name the other two radii like OP ?

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