# Important Questions for Class 9 Chapter 11 – Constructions

With such an exhaustive list of questions has step-by-step explanation and solutions for each question is also provided for your clear understanding and learning of the concepts. Download your free PDF now and start practicing.

Important questions based on NCERT syllabus for Chapter 11 - Constructions:

Question 1: Construct a Δ ABC in which AB = 4 cm, ∠ B = 60∘ and altitude CL = 3 cm. Construct a Δ ADE similar to Δ ABC such that each side of Δ ADE is 3/2 times that of the corresponding side of ΔABC
Solution:

Steps of construction:

1. Construct a Δ ABC with given measurement
2. Extend AB to D such that AD = 32, AB = (32 × 4) cm = 6 cm
3. Draw DE∥BC, cutting AC produced at E.
4. Δ ADE is the required triangle similar to Δ ABC such that each side of Δ ADE is 32 times the corresponding side of Δ ABC

Question 2: Draw a circle of radius 5 cm. Take a point P on it. Without using the centre of the circle construct a tangent at the point P.
Solution:

Steps of construction :

1. Draw a circle of radius 5 cm.
2. Mark a point P on it.
3. Draw any chord PQ.
4. Take a point R on the major arc QP.
5. Join PR and RQ.
6. Make ∠QPT = ∠PRQ [∵ Angles in the alternate segments are equal]
7. Produce TP to T', as shown in the figure.
8. T'PT is the required tangent at P.

Question 3: Construct a circle of radius 7cm. From a point 10 cm away from its centre, draw tangents to the circle.
Solution:

Steps of construction :

1. Draw a circle with 'O' as centre and radius 7 cm.
2. Mark a point P outside the circle such that OP = 10cm.
3. Draw a line segment from P to the centre of the circle O and bisect it. Let it be at a point, say M.
4. With M as centre and PM as radius draw a circle. Let this circle intersect the initial circle at points X and Y
5. Join PX and PY and extend them to X' and Y' respectively.
6. PX' and PY' are the required tangents.