ML Aggarwal Solution Class 10 Chapter 16 Constructions Exercise 16.1

 Exercise 16.1

Question 1

Use a ruler and compass only in this question. (i) Draw a circle, centre O and radius 4 cm. (ii) Mark a point P such that OP = 7 cm. Construct the two tangents to the circle from P. Measure and record the length of one of the tangents. 

Sol :

Steps of Construction:

1.Draw a circle with centre O and radius 4 cm.

2.Take a point P such that OP = 7 cm.

3.Bisect OB at M.

4.With centre M and diameter OP, draw another circle intersecting the given circle at A and B.

5.Join PA and PB. PA and PB is a pair of tangents to the circle.

6.On measuring PA, it is equal to 5.5 cm. 







Question 2

Draw a line AB = 6 cm. Construct a circle with AB as diameter. Mark a point P at a distance of 5 cm from the mid-point of AB. Construct two tangents from P to the circle with AB as diameter. Measure the length of each tangent 

Sol :

Steps of Construction:

1.Take a line segment AB = 6 cm.

2.Draw its perpendicular bisector bisecting it at O.

3.With centre O and radius OB, draw a circle.

4.Produce AB to P such that OP = 5 cm.

5.Draw its perpendicular bisector intersecting it at M.

6.With centre M and radius OM, draw a circle which intersects the given circle at T and S.

7.Join OT, OS, TP and SP. PT and PS are the required tangents to the given circle.

8.On measuring, each tangent is 4 cm long i.e. PT = PS = 4 cm.








Question 3

Construct a tangent to a circle of radius 4cm from a point on the concentric circle of radius 6 cm and measure its length. Also, verify the measurement by actual calculation. 

Sol :

Steps of construction:

1.Take a point O.

2.With centre O and radii 4 cm and 6 cm, draw two concentric circles.

3.Join OA and take its mid-point M.

4.With centre M and radius MA, draw another circle which intersects the first circle at P and Q.

5.Join AP and AQ. AP and AQ are the required tangents to the first circle from point A







Question 4

Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q. 

Sol :

Steps of construction:

1.Take a point O and with centre O, and radius 3 cm, draw a circle.

2.Produce its diameter both sides and cut off OP = OQ = 7 cm.

3.Take mid-points of OP and OQ as M and N respectively.

4.With centres M and N and OP and OQ as diameters, draw circles which intersect the given circle at A, B and C and D respectively.

5.Join PA, PB, QC and QD. PA, PB and QC and QD are the required tangents. 







Question 5

Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle. 

Sol :

Steps of construction:

1.Draw a line segment AB = 8 cm.

2.With centre A and radius 4 cm and with centre B and radius 3 cm, draw circles.

3.Draw a third circle AB as diameter which intersects the given two circles at C and D and P and Q respectively.

4.Join AC and AD, BP and BQ.

5.AC and AD, BP and BQ are the required tangents.




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