NCERT Exemplar solutions for Mathematics [English] Class 10 chapter 10 - Construction [Latest edition]

To divide a line segment AB in the ratio 5 : 7, first a ray AX is drawn so that ∠BAX is an acute angle and then at equal distances points are marked on the ray AX such that the minimum number of these points is ______.

To divide a line segment AB in the ratio 4 : 7, a ray AX is drawn first such that ∠BAX is an acute angle and then points A₁, A₂, A₃, .... are located at equal distances on the ray AX and the point B is joined to ______.

To divide a line segment AB in the ratio 5 : 6, draw a ray AX such that ∠BAX is an acute angle, then draw a ray BY parallel to AX and the points A₁, A₂, A₃, ... and B₁, B₂, B₃, ... are located at equal distances on ray AX and BY, respectively. Then the points joined are ______.

To construct a triangle similar to a given ΔABC with its sides `3/7` of the corresponding sides of ΔABC, first draw a ray BX such that ∠CBX is an acute angle and X lies on the opposite side of A with respect to BC. Then locate points B₁, B₂, B₃, ... on BX at equal distances and next step is to join ______.

To construct a triangle similar to a given ΔABC with its sides `8/5` of the corresponding sides of ΔABC draw a ray BX such that ∠CBX is an acute angle and X is on the opposite side of A with respect to BC. Then minimum number of points to be located at equal distances on ray BX is ______.

To draw a pair of tangents to a circle which are inclined to each other at an angle of 60°, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be ______.

By geometrical construction, it is possible to divide a line segment in the ratio `sqrt(3) : 1/sqrt(3)`.

To construct a triangle similar to a given ∆ABC with its sides `7/3` of the corresponding sides of ∆ABC, draw a ray BX making acute angle with BC and X lies on the opposite side of A with respect to BC. The points B₁, B₂, ...., B₇ are located at equal distances on BX, B₃ is joined to C and then a line segment B₆C' is drawn parallel to B₃C where C' lies on BC produced. Finally, line segment A'C' is drawn parallel to AC.

A pair of tangents can be constructed from a point P to a circle of radius 3.5 cm situated at a distance of 3 cm from the centre.

A pair of tangents can be constructed to a circle inclined at an angle of 170°.

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

Draw a right triangle ABC in which BC = 12 cm, AB = 5 cm and ∠B = 90°. Construct a triangle similar to it and of scale factor `2/3`. Is the new triangle also a right triangle?

Draw a triangle ABC in which BC = 6 cm, CA = 5 cm and AB = 4 cm. Construct a triangle similar to it and of scale factor `5/3`.

Construct a tangent to a circle of radius 4 cm from a point which is at a distance of 6 cm from its centre.

Two line segments AB and AC include an angle of 60° where AB = 5 cm and AC = 7 cm. Locate points P and Q on AB and AC, respectively such that AP = `3/4` AB and AQ = `1/4` AC. Join P and Q and measure the length PQ.

Draw a parallelogram ABCD in which BC = 5 cm, AB = 3 cm and ∠ABC = 60°, divide it into triangles BCD and ABD by the diagonal BD. Construct the triangle BD' C' similar to ∆BDC with scale factor `4/3`. Draw the line segment D'A' parallel to DA where A' lies on extended side BA. Is A'BC'D' a parallelogram?

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

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.

Draw a triangle ABC in which AB = 5 cm, BC = 6 cm and ∠ABC = 60°. Construct a triangle similar to ∆ABC with scale factor `5/7`. Justify the construction.

Draw a circle of radius 4 cm. Construct a pair of tangents to it, the angle between which is 60º. Also justify the construction. Measure the distance between the centre of the circle and the point of intersection of tangents.

Draw a triangle ABC in which AB = 4 cm, BC = 6 cm and AC = 9 cm. Construct a triangle similar to ∆ABC with scale factor `3/2`. Justify the construction. Are the two triangles congruent? Note that all the three angles and two sides of the two triangles are equal.