R.S. Aggarwal solutions for Mathematics [English] Class 10 chapter 9 - Constructions [Latest edition]

Draw a line segment AB of length 7 cm. Using ruler and compasses, find a point P on AB such that `(AP)/(AB) = 3/5`.

Draw a line segment of length 8 cm and divide it internally in the ratio 4 : 5.

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

Construct a ΔPQR, in which PQ = 6 cm, QR = 7 cm and PR = 8 cm. Then, construct another triangle whose sides are `4/5` times the corresponding sides of ΔPQR.

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.

Construct a ΔABC with BC = 6 cm, ∠B = 60° and AB = 5 cm. Construct another triangle whose sides are `3/4` times the corresponding sides of ΔАВС.

Construct a ΔABC in which AB = 6 cm, ∠A = 30° and ∠B = 60°. Construct another ΔAB'C' similar to ΔABC with base AB' = 8 cm.

Construct a ΔABC in which BC = 8 cm, ∠B = 45° and ∠C = 60°. Construct another triangle similar to ΔABC such that its sides are `3/5` of the corresponding sides of ΔABC.

To construct a triangle similar to ΔABC in which BC = 4.5 cm, ∠B = 45° and ∠C = 60°, using a scale factor of `3/7`, BC will be divided in the ratio

(a) 3 : 4 

(b) 4 : 7

(c) 3 : 10

(d) 3 : 7

Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are `1 1/2` times the corresponding sides of the isosceles triangle.

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

Draw a circle of radius 3 cm. Form a point P, 7 cm away from the centre of the circle, draw two tangents to the circle. Also, measure the lengths of the tangents.

Draw two tangents to a circle of radius 3.5 cm from a point P at a distance of 6.2 cm from its centre.

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

Draw a circle with center O and radius 4 cm. Draw any diameter AB of this circle. Construct tangents to the circle at each of the two end points of the diameter AB.

Draw a circle with the help of a bangle. Take any point P outside the circle. Construct the pair of tangents from the point P to the circle.

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

Draw a circle of radius 4.2 cm. Draw a pair of tangents to this circle inclined to each other at an angle of 45°.

Write the steps of construction for drawing a pair of tangents to a circle of radius 3 cm, which are inclined to each other at an angle of 60°.

Draw a circle of radius 3 cm. Draw a tangent to the circle making an angle of 30° with a line passing through the centre.

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.

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 inner circle.

Write the steps of construction to construct the tangents to a circle from an external point.

Draw a circle of radius 3 cm with centre O and take a point P outside the circle such that OP = 6.5 cm. From P, draw two tangents to the circle.

Draw a line segment AB of length 5.4 cm. Divide it into six equal parts. Write the steps of construction.

Draw a line segment AB of length 6.5 cm and divide it in the ratio 4 : 7. Measure each of the two parts.

Construct a ΔABC in which BC = 6.5 cm, AB = 4.5 cm and ∠ABC = 60°. Construct a triangle similar to this triangle whose sides are `3/4` of the corresponding sides of ΔABC.

Construct a ΔABC in which BC = 5 cm, ∠C = 60° and altitude from A equal to 3 cm. Construct a ΔADE similar to ΔABC such that each side of ΔADE is `3/2` times the corresponding side of ΔABC. Write the steps of construction.

Construct an isosceles triangle whose base is 9 cm and altitude 5 cm. Construct another triangle whose sides are `3/4` of the corresponding sides of the first isosceles triangle.

Draw a ΔABC, right-angled at B such that AB = 3 cm and BC = 4 cm. Now, construct a triangle similar to ΔABC, each of whose sides is `7/5` times the corresponding side of ΔАВС.

Draw a circle of radius 4.8 cm. Take a point P on it. Without using the centre of the circle, construct a tangent at the point P. Write the steps of construction.

Draw a circle of radius 3.5 cm. Draw a pair of tangents to this circle which are inclined to each other at an angle of 60°. Write the steps of construction.

Draw a circle of radius 4 cm. Draw tangent to the circle making an angle of 60° with a line passing through the centre.

Draw two concentric circles of radii 4 cm and 6 cm. Construct a tangent to the smaller circle from a point on the larger circle. Measure the length of this tangent.