Chapter 11: Constructions

VVI questions — the ones the board asked most (8)

1. Q1Long answer5 marksAsked: 2025

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

   

   Medha Ma’am

   AskMedha’s AI teacher

   Hear it from Medha Ma’am · 130 s

   Model answer · division of line segment, construction

   1. 1.To divide a line segment of length 7.6 cm in the ratio 5 : 8, first draw a line segment AB of length 7.6 cm using a ruler.1 mark
   2. 2.Draw any ray AX making an acute angle with AB.1 mark
   3. 3.Since we have to divide AB in the ratio 5 : 8, locate 13 (= 5 + 8) points A1, A2, A3, A4, A5, A6, A7, A8, A9, A10, A11, A12, A13 on the ray AX so that AA1 = A1A2 = A2A3 = A3A4 = A4A5 = A5A6 = A6A7 = A7A8 = A8A9 = A9A10 = A10A11 = A11A12 = A12A13, marking 13 equal arcs on the ray AX.1 mark
   4. 4.Join A13 to B. Through the point A5, draw a line parallel to A13B, by making an angle equal to ∠AA13B at A5, so that this parallel line intersects AB at the point P. By the Basic Proportionality Theorem, since A5P is parallel to A13B, AA5/A5A13 = AP/PB, and by construction AA5/A5A13 = 5/8, therefore AP/PB = 5/8. This shows that P divides AB in the ratio 5 : 8.1 mark
   5. 5.On measuring the two parts of the line segment AB with a ruler, we get AP = 2.9 cm and PB = 4.7 cm.1 mark

   Diagram: Draw line segment AB = 7.6 cm with ray AX at an acute angle from A; mark 13 equal points A1 to A13 on AX; join A13 to B; draw A5P parallel to A13B meeting AB at P; label A, B, P, A5, A13, and X on the figure.

   • Write 'acute angle' when describing ray AX.
   • State clearly that 5 + 8 = 13 equal arcs are marked on AX.
   • Name the point of intersection as P and give measured lengths AP = 2.9 cm and PB = 4.7 cm with units.

   Marks split from a structure derived from past papers (checked twice); not Bihar Board’s official scheme

2. Q2Long answer5 marksAsked: 2026

   Construct a triangle ABC in which BC = 6 cm, AB = 5 cm and angle ABC = 60°. Then construct a triangle whose sides are 5/7 times the corresponding sides of the triangle ABC.

   

   Medha Ma’am

   AskMedha’s AI teacher

   Hear it from Medha Ma’am · 125 s

   Model answer · construction, similar triangle scale factor

   1. 1.A line segment BC of length 6 cm is drawn first.1 mark
   2. 2.At point B, an angle of 60° is constructed with BC, that is ∠ABC = 60°, and on the ray forming this angle, a line segment AB of length 5 cm is marked to locate point A.1 mark
   3. 3.A is then joined to C by drawing the line segment AC, which completes the triangle ABC with BC = 6 cm, AB = 5 cm and ∠ABC = 60°.1 mark
   4. 4.To construct a triangle whose sides are 5/7 of the corresponding sides of triangle ABC, a ray BX is drawn making an acute angle with BC on the side opposite to the vertex A. Since 5/7 has 7 as the greater of 5 and 7, 7 points B1, B2, B3, B4, B5, B6 and B7 are located on BX such that BB1 = B1B2 = B2B3 = B3B4 = B4B5 = B5B6 = B6B7, all equal parts.1 mark
   5. 5.B7 is joined to C, and since 5 is the smaller of 5 and 7, a line is drawn through B5 parallel to B7C, intersecting BC (or its extension) at C′. A line through C′ parallel to CA is drawn, intersecting BA (or its extension) at A′. Then A′BC′ is the required triangle, whose sides are 5/7 of the corresponding sides of triangle ABC.1 mark

   Diagram: Draw triangle ABC with BC = 6 cm, AB = 5 cm, ∠ABC = 60°, and AC joined; from B draw ray BX at an acute angle to BC with 7 equal points B1 to B7 marked; join B7C, draw B5C′ parallel to B7C meeting BC at C′, then draw C′A′ parallel to CA meeting BA at A′; label B, C, A, B1–B7, C′, A′ and triangle A′BC′ as the required triangle.

   • Write '∠ABC = 60°' explicitly while marking the angle at B, not just 'angle at B'.
   • State that B7 is joined to C and the line through B5 is drawn parallel to B7C, naming both points.
   • Mention that 7 equal parts are marked on BX since 7 is the greater of 5 and 7 in the scale factor 5/7.

   Marks split from a structure derived from past papers (checked twice); not Bihar Board’s official scheme

3. Q3Long answer5 marksAsked: 2022

   Draw a circle of radius 6 cm. From a point 10 cm away from its centre construct a pair of tangents to the circle.

   

   Medha Ma’am

   AskMedha’s AI teacher

   Hear it from Medha Ma’am · 45 s

   Model answer · construction, pair of tangents to a circle

   1. 1.Draw a circle with centre O and radius 6 cm.1 mark
   2. 2.Mark a point P outside the circle at a distance of 10 cm from O and join OP.1 mark
   3. 3.Draw the perpendicular bisector of OP to obtain its midpoint M.1 mark
   4. 4.Taking M as centre and MO as radius, draw an auxiliary circle. Let it intersect the given circle at the points E and F.1 mark
   5. 5.Join PE and PF. Then PE and PF are the required pair of tangents from the external point P to the circle.1 mark

   Diagram: Draw circle with centre O, radius 6 cm; mark point P with OP = 10 cm; draw perpendicular bisector of OP meeting it at M; draw auxiliary circle with centre M and radius MO cutting the given circle at E and F; draw and label lines PE and PF as the required tangents.

   • Clearly write 'OP' and the length '10 cm' when marking point P.
   • Label the two intersection points of the auxiliary circle with the given circle as 'E' and 'F'.
   • Write 'PE' and 'PF' as the names of the required tangents in the last step.

   Marks split from a structure derived from past papers (checked twice); not Bihar Board’s official scheme

4. Q4Long answer5 marksAsked: 2022

   Draw a circle inside an equilateral triangle of side 5 cm which touches the sides of the triangle.

   How the model answer begins

   1. First, an equilateral triangle ABC of side 5 cm is constructed. Draw a line segment BC = 5 cm. With B as centre and radius 5 cm, draw an arc. With C as centre and radius 5 cm, draw another arc to intersect the first arc…

   The full answer from Medha Ma’am →
5. Q5Long answer5 marksAsked: 2022

   Construct a triangle ABC in which BC = 6 cm, AB = 5 cm and angle ABC = 60 degree; then construct a similar triangle whose sides are 3/4 times the corresponding sides of triangle ABC.

   How the model answer begins

   1. First, draw a line segment BC = 6 cm as the base of the required triangle.

   The full answer from Medha Ma’am →
6. Q6Long answer5 marksAsked: 2023

   Draw a right angled triangle ABC in which AB = 6 cm, BC = 8 cm and angle B = 90°, D is the foot of perpendicular BD from B on AC. Draw circumcircle of ABCD and draw a tangent from A on this circle.

   How the model answer begins

   1. Draw BC = 8 cm; at B make an angle of 90° and cut BA = 6 cm on it; join AC. ABC is the required right triangle.

   The full answer from Medha Ma’am →
7. Q7Long answer5 marksAsked: 2023

   Draw a right angled triangle ABC in which AB = 6 cm, BC = 8 cm and angle B = 90°. D is the foot of perpendicular BD from B on AC. Draw circumcircle of ABCD and draw a tangent from A on this circle.

   How the model answer begins

   1. Draw BC = 8 cm; at B make 90° and cut BA = 6 cm; join AC — right triangle ABC with ∠B = 90°.

   The full answer from Medha Ma’am →
8. Q8Long answer5 marksAsked: 2021

   Construct a triangle ABC in which AB = 5 cm, BC = 6 cm and AC = 7 cm. Then construct a triangle similar to triangle ABC whose sides are 5/7 times the corresponding sides of triangle ABC.

   How the model answer begins

   1. Triangle ABC is constructed by first drawing side BC = 6 cm. Then with B as centre and radius AB = 5 cm, an arc is drawn, and with C as centre and radius AC = 7 cm, another arc is drawn to intersect the first arc at…

   The full answer from Medha Ma’am →

Questions parents and students ask

How many marks does "Constructions" carry in Bihar Board Class 10 Maths?

In the Bihar Board papers of 2021–2026, this chapter carried about 2 marks and about 1 questions a year; by marks it ranks 15 in Maths.

Which are the most important (VVI) questions of "Constructions"?

The 8 questions above are from the board’s real papers, each with the years it was asked; the most-asked come first with their full model answers. All 8 written questions of this chapter, with answers, are in the AskMedha app.

Do the answers follow the board’s marking scheme?

BSEB does not publish a marking scheme. Each answer is written point by point on a structure derived from past papers and checked by a second, independent model; it is never called the board’s official scheme.