RD Sharma Solutions for Class 10 Maths Chapter 11 – Constructions

RD Sharma Solutions for Class 10 Maths Chapter 11 – Constructions are available here to help students master the art of accurate geometrical drawing. Scoring good marks in Mathematics requires consistent practice, a strong grasp of concepts, and the correct approach to problem-solving. 

To support students in this journey, the expert team at Infinity Learn has developed detailed RD Sharma Solutions, offering clear explanations and step-by-step methods for attempting construction-based questions effectively.

These solutions are essential for all students aiming for an in-depth understanding of the subject, efficient last-minute revision, and a quick recall of important formulas and construction techniques.

Chapter 11 – Constructions from RD Sharma Class 10 Solutions features three exercises focused on practical geometry skills. By referring to these solutions, students can learn the correct procedures and presentation styles required to solve construction problems confidently in their exams.

The key topics covered in this chapter include:

• Division of a line segment into a given ratio
• Construction of a triangle similar to a given triangle based on a specific scale factor
• Construction of tangents to a circle from an external point

Practicing with RD Sharma Solutions for Class 10 Constructions ensures that students not only understand the theoretical concepts but also perfect the precision and accuracy needed to excel in board examinations.

Download RD Sharma for Class 10 Maths Chapter 11 Constructions PDF here

Access Answers to Maths RD Sharma Solutions For Class 10 Chapter 11 – Constructions

1. Divide a line segment of 8 cm internally in the ratio 3:5.

Solution:

• Draw a line segment AB = 8 cm.
• Draw a ray AX making an acute angle with AB.
• Mark 8 equal divisions on AX (since 3 + 5 = 8 parts).
• Label them A₁, A₂, ..., A₈.
• Join A₈ to B.
• Draw a line through A₃ parallel to A₈B using a compass and ruler.
• Let this line meet AB at point P.
• Point P divides AB internally in the ratio 3:5.

2. Divide a line segment of 10 cm internally in the ratio 2:3.

Solution:

• Draw AB = 10 cm.
• Draw ray AX making any acute angle with AB.
• Mark 5 equal parts (2 + 3 = 5) on AX.
• Join the last point A₅ to B.
• Draw a line through A₂ parallel to A₅B to meet AB at P.
• P divides AB internally in the ratio 2:3.

3. Divide a line segment of 6 cm in the ratio 4:1 internally.

Solution:

• Draw AB = 6 cm.
• Draw a ray AX making an acute angle with AB.
• Mark 5 equal divisions (4 + 1 = 5) on AX.
• Connect A₅ to B.
• Draw a line through A₄ parallel to A₅B to meet AB at P.
• P is the required point.

4. Construct a triangle similar to a given triangle with sides in the ratio 2:3.

Solution:

• Draw the given triangle ABC.
• Draw a ray AX at A making an acute angle with AB.
• Mark 3 equal parts on AX.
• Join A₃ to B.
• Draw A₂B' parallel to A₃B.
• Through B', draw a line parallel to BC to meet AC at C'.
• ΔAB'C' is the required triangle similar to ΔABC in the ratio 2:3.

5. Construct a triangle similar to a given triangle in the ratio 5:4.

Solution:

• Draw triangle ABC.
• Draw ray AX at A making an acute angle with AB.
• Mark 5 equal divisions.
• Join A₅ to B.
• Draw A₄B' parallel to A₅B.
• Through B', draw B'C' parallel to BC meeting AC at C'.
• ΔAB'C' is the required triangle similar to ΔABC in the ratio 5:4.

6. Divide a line segment of 12 cm internally in the ratio 7:5.

Solution:

• Draw AB = 12 cm.
• Draw ray AX making an acute angle with AB.
• Mark 12 equal divisions.
• Join A₁₂ to B.
• Draw a line through A₇ parallel to A₁₂B.
• The point of intersection P divides AB in the ratio 7:5.

7. Divide a line segment of 9 cm in the ratio 1:2.

Solution:

• Draw AB = 9 cm.
• Draw an acute angled ray AX.
• Divide AX into 3 equal parts.
• Join A₃ to B.
• Draw A₁P parallel to A₃B.
• P divides AB in the ratio 1:2.

Exercise 11.2 – Construction of Similar Triangles

8. Construct a triangle similar to a given triangle with ratio 3:5.

Solution:

• Construct ΔABC.
• Draw ray AX at A.
• Mark 5 equal divisions.
• Join A₅ to B.
• Draw A₃B' parallel to A₅B.
• Then B'C' parallel to BC.
• ΔAB'C' is the required triangle similar to ΔABC in ratio 3:5.

9. Construct a triangle similar to a given triangle whose sides are in the ratio 4:3.

Solution:

• Same method as above but using 4 and 3 divisions.
• Join A₄ to B.
• Then A₃B' parallel to A₄B.
• Draw B'C' parallel to BC.
• ΔAB'C' is required.

10. Construct a triangle similar to a given triangle whose sides are in the ratio 7:3.

Solution:

• Draw ΔABC.
• Draw an acute ray at A.
• Mark 7 equal parts.
• Join A₇ to B.
• Draw A₃B' parallel to A₇B.
• Then B'C' parallel to BC.

11. Construct a triangle similar to a given triangle whose sides are in the ratio 2:5.

Solution:

• Draw ΔABC.
• Draw a ray at A.
• Mark 5 equal divisions.
• Join A₅ to B.
• Draw A₂B' parallel to A₅B.
• Then B'C' parallel to BC.

12. Construct a triangle similar to a given triangle whose sides are in the ratio 6:5.

Solution:

• Draw ΔABC.
• Draw a ray at A making an acute angle.
• Mark 6 equal parts.
• Join A₆ to B.
• Draw A₅B' parallel to A₆B.

13. Divide a line segment of 15 cm in the ratio 2:3.

Solution:

• Draw AB = 15 cm.
• Draw a ray AX.
• Divide AX into 5 parts.
• Join A₅ to B.
• Draw A₂P parallel to A₅B.

Exercise 11.3 – Construction of Tangents to a Circle

14. Construct a tangent to a circle from a point outside the circle.

Solution:

• Draw the circle with center O.
• Take external point P.
• Join OP.
• Find midpoint of OP and draw a circle with center at midpoint and radius = OP/2.
• This new circle intersects original circle at points T₁ and T₂.
• Draw PT₁ and PT₂.
• These are required tangents.

15. Construct two tangents to a circle from an external point.

Solution:

• Draw the given circle with center O.
• Take an external point P.
• Join OP.
• Draw perpendicular bisector of OP.
• Let M be midpoint.
• With M as center, radius = OM, draw a circle.
• The circle cuts given circle at points T₁ and T₂.
• PT₁ and PT₂ are the required tangents.

16. Draw a pair of tangents from a point 5 cm away from center of circle with radius 3 cm.

Solution:

• Draw a circle of radius 3 cm.
• Mark point P, 5 cm away from center.
• Join OP.
• Draw the perpendicular bisector of OP.
• Draw a circle with center at midpoint of OP and radius = OP/2 = 2.5 cm.
• Draw tangents from P to points of contact.

17. Construct a tangent to a circle of radius 4 cm from a point 7 cm away.

Solution:

• Draw a circle of radius 4 cm.
• Locate external point P at 7 cm.
• Join OP.
• Find midpoint, draw another circle.
• Draw tangents from P to circle.

18. Construct two tangents from a point 10 cm away to a circle of radius 6 cm.

Solution:

• Draw a circle of radius 6 cm.
• Locate point P at 10 cm from center.
• Join OP.
• Draw perpendicular bisector.
• Construct tangents as explained above.

19. Construct a circle and draw two tangents from an external point without measuring distance.

Solution:

• Draw circle.
• Mark external point.
• Join OP.
• Draw perpendicular bisector of OP.
• Construct auxiliary circle.
• Draw two tangents from external point.

20. Draw a tangent to a circle from a point on the circle itself.

Solution:

• Draw circle with center O.
• Mark point P on circumference.
• Draw radius OP.
• Draw tangent at point P perpendicular to radius OP.