### 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. 3.1

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 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

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