**Important questions for Class 10 Maths Chapter 11 Constructions** are provided here based on the new pattern of CBSE for 2019-2020. Students who are preparing for the board exams of 2020 can practice these questions of Construction For Class 10 to score full marks for the questions from this chapter.

The chapter Constructions deals with the construction of line segments, construction of similar triangle with the given scale factor and the construction of tangents to the circle. Students can also refer to these important questions as a part of their board exam preparation. NCERT Solutions are also available at BYJU’S to help the students in scoring full marks.

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## Important Questions & Answers For Class 10 Maths Chapter 11 Constructions

**Q.1: Draw a line segment of length 7 cm. Find a point P on it which divides it in the ratio 3:5.**

Solution:

Steps of construction:

1. Draw a line segment, AB = 7 cm.

2. Draw a ray, AX, making an acute angle downward with AB.

3. Mark the points A_{1}, A_{2}, A_{3} … A_{8} on AX.

4. Mark the points such that AA_{1} = A_{1}A_{2} = A_{2}A_{3} = ….., A_{7}A_{8}.

5. Join BA_{8}.

6. Draw a line parallel to BA_{8} through the point A_{3}, to meet AB on P.

Hence AP: PB = 3: 5

**Q.2: Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are 7/5 of the corresponding sides of the first triangle.**

Solution:

Steps of Constructions:

- Draw a line segment AB =5 cm.
- Take A and B as centre, and draw the arcs of radius 6 cm and 5 cm respectively.
- These arcs will intersect each other at point C and therefore ΔABC is the required triangle with the length of sides as 5 cm, 6 cm, and 7 cm respectively.
- Draw a ray AX which makes an acute angle with the line segment AB on the opposite side of vertex C.
- Locate the 7 points such as A
_{1}, A_{2}, A_{3}, A_{4}, A_{5}, A_{6}, A_{7}(as 7 is greater between 5and 7), on line AX such that it becomes AA_{1}= A_{1}A_{2}= A_{2}A_{3}= A_{3}A_{4}= A_{4}A_{5}= A_{5}A_{6}= A_{6}A_{7}. - Join the points BA
_{5}and draw a line from A_{7}to BA5 which is parallel to the line BA5 where it intersects the extended line segment AB at point B’. - Now, draw a line from B’ the extended line segment AC at C’ which is parallel to the line BC and it intersects to make a triangle.

Therefore, ΔAB’C’ is the required triangle.

**Q.3: 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.**

Solution:

Steps of construction:

- Draw a circle with a radius of 3 cm with centre “O”.
- Draw a diameter of a circle and it extends 7 cm from the centre and mark it as P and Q.
- Draw the perpendicular bisector of the line PO and mark the midpoint as M.
- Draw a circle with M as centre and MO as the radius
- Now join the points PA and PB in which the circle with radius MO intersects the circle of circle 3cm.
- Now PA and PB are the required tangents.
- Similarly, from the point Q, we can draw the tangents.
- From that, QC and QD are the required tangents.

**Q. 4: Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle.**

Solution:

Steps of construction:

- Draw a circle with the help of a bangle.
- Draw two non-parallel chords such as AB and CD
- Draw the perpendicular bisector of AB and CD
- Take the centre as O where the perpendicular bisector intersects.
- To draw the tangents, take a point P outside the circle.
- Join the points O and P.
- Now draw the perpendicular bisector of the line PO and midpoint is taken as M
- Take M as centre and MO as radius draw a circle.
- Let the circle intersects intersect the circle at the points Q and R
- Now join PQ and PR
- Therefore, PQ and PR are the required tangents.

**Q. 5: Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on the outer circle construct the pair of tangents to the other. Measure the length of a tangent and verify it by actual calculation.**

**Solution:**

Steps of construction:

- Draw a circle with centre O and radius 3 cm.
- Draw another circle with centre O and radius 5 cm.
- Take a point P on the circumference of a larger circle and join OP.
- Draw another circle with diameter OP such that it intersects the smallest circle at A and B.
- Join A to P and B to P.

Hence AP and BP are the required tangents.

### Practice Questions For Class 10 Maths Chapter 11 Constructions

- Draw an isosceles triangle ABC in which AB = AC = 6 cm and BC = 5 cm. Construct a triangle PQR similar to ∆ ABC in which PQ = 8 cm. Also, justify the construction.
- Let ABC be a right triangle in which AB = 6 cm, BC = 8 cm and ∠ B = 90°. BD is perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle.
- Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.
- Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct a triangle whose sides are 3/4 of the corresponding sides of the triangle ABC.
- Draw a triangle PQR with side QR = 7 cm, angle Q = 45 degrees and Angle A = 105 degree. After that, Construct a triangle whose sides are 3/4 of the corresponding sides of triangle ABC.
- Use a bangle to draw a circle and take a point outside the circle. Now construct a pair of tangents from A to this circle.
- Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts.
- Draw a pair of tangents to a circle of radius 5 cm which is inclined to each other at an angle of 60 degrees.