# Important Questions for Chapter 11 - Constructions

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**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:

- Construct a Δ ABC with given measurement
- Extend AB to D such that AD = 32, AB = (32 × 4) cm = 6 cm
- Draw DE∥BC, cutting AC produced at E.
- 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 :

- Draw a circle of radius 5 cm.
- Mark a point P on it.
- Draw any chord PQ.
- Take a point R on the major arc QP.
- Join PR and RQ.
- Make ∠ QPT = ∠ PRQ [∵ Angles in the alternate segments are equal]
- Produce TP to T', as shown in the figure.
- 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 :

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