CONSTRUCTION

BASIC CONSTRUCTION


To draw a perpendicular bisector of a given line segment.


To draw an angle bisector of a given angle.


To draw a perpendicular to a line at a given point on it.


To draw a perpendicular to a given line from a point outside it.


To draw an angle congruent to a given angle.


To draw a line parallel to a given line through a point outside it.



Ex. No. 3.1 


1. Draw the circumcircle of  ∆ PMT such that, PM = 5.4 cm, P = 60º,   M = 70º.  [Ans.]

2. Construct the circumcircle of  ∆ SIM in which SI = 6.5 cm,  ∠ I = 125º, IM = 4.4 cm.  [Ans.]

3.  Construct the circumcircle of  ∆ KLM in which KM = 7 cm, ∠ K = 60º, ∠ M = 55º. [Ans.]

4. Construct a right angled triangle  ∆PQR where PQ = 6 cm,  ∠QPR = 40º, ∠PRQ = 90º. Draw circumcircle of ∆ PQR.  [Ans.]

5. Construct the incircle of ∆RST in which RS = 6 cm, ST = 7 cm and RT = 6.5 cm. [Ans.]

6. Construct the incircle of  ∆ STU in which, ST = 7 cm,  ∠T = 120º, TU = 5 cm. [Ans.]

7. Construct the incircle of  ∆DEF in which DE = DF = 5.8 cm, ∠EDF = 65º. [Ans.]


8. Construct any right angled triangle and draw incircle of that triangle. [Ans.]



9. Construct the circumcircle and incircle of an equilateral ∆ XYZ with side 6.3 cm. [Ans.]


Ex. No. 3.2

1. Draw a tangent at any point ‘M’ on the circle of radius 2.9 cm and centre ‘O’.[Ans.]

2. Draw a tangent at any point R on the circle of radius 3.4 cm and centre ‘P’. [Ans.]

3. Draw a circle of radius 2.6 cm. Draw tangent to the circle from any point on the circle using centre of the circle. [Ans.]

4. Draw a circle with centre P and radius 3.1 cm. Draw a chord MN of length 3.8 cm. Draw tangent to the circle through points M and N. [Ans.]

5. Draw a circle of radius 3.5 cm. Take any point K on it. Draw a tangent to the circle at K without using the centre of the circle. [Ans.]

6. Draw a circle of radius 2.7 cm and draw chord PQ of length 4.5 cm. Draw tangents at P and Q without using centre. [Ans.]

7. Draw a circle having radius 3 cm draw a chord XY = 5 cm. Draw tangents at point X and Y without using centre.[Ans.]

8. Draw a tangent to the circle from the point B, having radius 3.6 cm and centre ‘C’. Point B is at a distance 7.2 cm from the centre. [Ans.]

9. Draw a tangent to the circle from the point L with radius 2.8 cm. Point ‘L’ is at a distance 5 cm from the centre ‘M’. [Ans.]


10. Draw a tangent to the circle with centre O and radius 3.3 cm from a point A such that d (O, A) = 7.5 cm. Measure the length of tangent segment. [Ans.]


Exercise No. 3.3. 

1. Sum No. 1. [video]

5. Sum No. 5 [video]

6. Sum No. 6 [Video]



Problem Set No. 3

1. Draw an angle of 125º and bisect it.


2. Draw perpendicular bisector of seg AB of length 8.3 cm.