Solution of Chapter 10. Constructions (NCERT - Mathematics Exemplar Book)

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 to equal distances on ray AX and BY, respectively. Then the points joined are

To construct a triangle similar to a given ∆ABC with its sides 3/7 of the corresponding sides of ∆ABC, 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 ∆ABC with its sides 8/5 of the corresponding sides of ∆ABC draw a ray BX such that ∠CBX is an acute angle and X is on the opposite side of A with respect to BC. The 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 endpoints 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 .

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 an acute angle with BC and X lies on the opposite side of A with respect of BC. The points B₁, B₂,...........B₁ are located at equal distances on BX, B₃ is joined to C and then a where C’ lines on BC produced. Finally line segment A’C’ is drawn parallel to AC.

A parallel 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 center.

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

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

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

Thinking process

Here scale factor i.e., m>n then the triangle to be constructed is larger than the given triangle. Use this concept and then constant the required triangle.

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

Two-line segment AB and AC include an angle of 60°, where AB=5cm and AC=7cm. 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 triangles 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 ∆ABC in which AB=5 cm, BC=6 cm, and ∠ABC=60°. Construct a triangle similar to ABC with scale factor Justify the construction.

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

Draw a ∆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.