Worksheet on Constructions for Class 10

Precise drawings require mathematical skill and knowledge and these printable grade 10 constructions practice questions teach geometric drawing techniques. Students learn to create accurate shapes using a compass and a ruler. Each exercise develops precision while building spatial understanding. These activities prepare learners for technical drawing and engineering applications. Download free Class 10 constructions PDF worksheet for geometric precision.

Solved Questions based on Construction

1. Which of the following steps of construction is INCORRECT while constructing a circumscribing circle of an equilateral triangle ABC of side 5 cm?

Step 1: Draw a line segment AB = 5 cm.

Step 2: With A and B as the centres, draw arcs of radius 5 cm intersecting each other at C.

Step 3: Join AC and BC. △ABC is an equilateral triangle.

Step 4: Draw the median of AB and AC that intersect each other at O.

Step 5: Join OA.

Step 6: With O as the centre and OA as the radius, draw a circle passing through A, B and C.

a) Step 2
b) Step 6
c) Step 4
d) Step 3

Answer: c) Step 4

Explanation: Consider the figure given below:

The steps to construct a circumscribing circle of an equilateral triangle ABC of side 5 cm are:

Step 1: Draw a line segment AB = 5 cm.

Step 2: With A and B as the centres, draw arcs of radius 5 cm intersecting each other at C.

Step 3: Join AC and BC. △ABC is an equilateral triangle.

Step 4: Draw the perpendicular bisectors of side AB and AC intersecting each other at O.

Step 5: Join OA.

Step 6: With O as the centre and OA as the radius, draw a circle passing through A, B and C.

2. If the angle bisectors of angles P and R of a triangle PQR meet at O, then what is the point O called?

a) Centroid
b) Orthocentre
c) Circumcentre
d) Incentre

Answer: d) Incentre

Explanation:

1. Incentre: The incentre of a triangle is where the three angle bisectors meet. It is like the centre of a circle that fits inside the triangle perfectly and touches all three sides.
   
2. Circumcentre: The circumcentre is a point where the perpendicular bisectors of the three sides of a triangle intersect. It is the centre of a circle that passes through all three vertices of the triangle.
   
3. Orthocentre: The orthocentre is a point where the three altitudes of a triangle intersect. It is where the lines drawn straight up from each corner meet.
   
4. Centroid: The centroid is a point where the three medians (lines joining each vertex to the midpoint of the opposite side) of a triangle intersect.
   

3. What is the measure of each internal angle of a regular hexagon?

a) 100°
b) 110°
c) 120°
d) 130°

Answer: c) 120°

Explanation: The interior angle of the regular polygon of n sides is given by:

Each interior angle = $\frac{\frac{\mathrm{2n\; -\; 4}}{}}{\frac{n}{}}$ × 90°

A regular hexagon has 6 sides.

Thus, n = 6

Each interior angle of a regular hexagon = $\frac{\frac{\mathrm{2n\; -\; 4}}{}}{\frac{n}{}}$ × 90°
                                                           = $\frac{\frac{\mathrm{2(6)\; -\; 4}}{}}{\frac{6}{}}$ × 90°
                                                           = (12 − 4) × 15°
                                                           = 8 × 15°
                                                           = 120°

Each interior angle of a regular hexagon = 120°

4. What will be the radius of the circle circumscribing an equilateral triangle of side 4.5 cm constructed using a ruler and compass?

a) 2.4 cm
b) 2.6 cm
c) 3.4 cm
d) 3.6 cm

Answer: b) 2.6 cm

Explanation: Construct the figure using the given steps:

Steps of Construction:

Step 1: Make a line segment BC of length 4.5 cm.
Step 2: Use points B and C as centres and draw two arcs with a radius of 4.5 cm intersecting each other at point A.
Step 3: Join AC and AB.
Step 4: Draw the perpendicular bisectors of AC and BC intersecting each other at O.
Step 5: Using O as the centre and OA, OB or OC as the radius, draw a circle. This circle will pass through points A, B, and C.
Step 6: This is the required circumcircle of triangle ABC. After measuring, the radius is OA is 2.6 cm.

5. Arrange the given steps for constructing an inscribing circle of a regular hexagon of side 6 cm in CORRECT order.

Steps of Construction:

Step 1: At points A and B, draw the angle bisectors of angles A and B intersecting each other at point O.
Step 2: With O as the centre and OL as the radius, draw a circle touching the hexagon's sides.
Step 3: Draw a line segment AB of length 6 cm.
Step 4: From O, draw OL perpendicular to AB.
Step 5: At points F and C, draw rays making an angle of 120° each. These lines cut off segments FE and CD, both measuring 6 cm.
Step 6: Draw rays making an angle of 120° each at points A and B. These lines cut off segments AF and BC, each measuring 6 cm.
Step 7: Join DE. Thus, ABCDEF is the required regular hexagon.

a) 3 - 5 - 6 - 1 - 7 - 4 - 2
b) 3 - 1 - 6 - 5 - 7 - 4 - 2
c) 3 - 6 - 5 - 7 - 1 - 4 - 2
d) 3 - 1 - 5 - 6 - 7 - 4 - 2

Answer: c) 3 - 6 - 5 - 7 - 1 - 4 - 2

Explanation: 

Steps of Construction:

Step 1: Draw a line segment AB of length 6 cm.
Step 2: Draw rays making an angle of 120° each at points A and B. These lines cut off segments AF and BC, each measuring 6 cm.
Step 3: At points F and C, draw rays making an angle of 120° each. These lines cut off segments FE and CD, both measuring 6 cm.
Step 4: Join DE. Thus, ABCDEF is the required regular hexagon.
Step 5: At A and B, draw the angle bisectors of angles A and B intersecting each other at point O.
Step 6: From O, draw OL perpendicular to AB.
Step 7: With O as the centre and OL as the radius, draw a circle touching the hexagon's sides. Thus, this circle is the required incircle.

Construct the figure using the given steps: