# NCERT Solutions for class 10th Maths Chapter 11 Constructions

### Exercise 11.1

In each of the following, give the justification of the construction also:

Question 1. Draw a line segment of length 7.6 cm and divide it in the ratio 5: 8. Measure the two parts.

Question 2. Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are 2/3 of the corresponding sides of the first triangle.

Question 3. 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.

Question 4. Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are 11/2 times the corresponding sides of the isosceles triangles.

Question 5. Draw a triangle ABC with side BC= 6 cm, AB= 5 cm and LABC =60Â°. Then construct a triangle whose sides are 3/4 of the corresponding sides of the triangle ABC.

Question 6. Draw a triangle ABC with side BC = 7 cm, LB = 45Â°, LA= 105Â°. Then, construct a triangle whose sides are 4/3 times the corresponding sides of MBC.

Question 7. Draw a right triangle in which the sides other than the hypotenuse are of lengths 4cm and 3cm. Then construct another triangle whose sides are 5/3 times the corresponding sides of the given triangle.

### Exercise 11.2

In each of the following, given the justification of the construction.

Question 1. Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct a pair of tangents to the circle and measure their lengths.

Note: If centre of the circle is not given, then locate the centre first by taking two nonÂ­ parallel chords and then finding the point of intersection of their perpendicular bisectors.

Question 2. Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation.

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

Question 4. Draw a pair of tangents to a circle of radius 5 cm, which are inclined to each other at an angle of 60Â°.

Question 5. Draw a line segment AB of length 8 cm. Taking A as the centre, draw a circle of radius 4 cm and taking B as the centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.

Question 6. Let ABC be a right triangle in which AB= 6 cm, BC= 8 cm and LB= 90Â°. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle.

Question 7. 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.

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