M l aggarwal understanding icse mathematics class 10 Solutions for Chapter 15 constructions

Exercises in Chapter 15 constructions Grade 10

Constructions Exercise 16.1

Constructions Exercise 16.2

Questions in Constructions Exercise 16.1

Use a ruler and compass only in this question.

Draw a circle, centre O and radius 4 cm.

Use a ruler and compass only in this question.

Mark a point P such that OP = 7 cm.

Construct the two tangents to the circle from P. Measure and record the length of one of the tangents.

Draw a line AB = 6 cm. Construct a circle with AB as diameter. Mark a point P at a distance of 5 cm from the mid-point of AB. Construct two tangents from P to the circle with AB as diameter. Measure the length of each tangent.

Construct a tangent to a circle of radius 4cm from a point on the concentric circle of radius 6 cm and measure its length. Also, verify the measurement by actual calculation.

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

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.

Questions in Constructions Exercise 16.2

Draw an equilateral triangle of side 4 cm. Draw its circumcircle.

Using a ruler and a pair of compasses only, construct:

A triangle ABC given AB = 4 cm, BC = 6 cm and ∠ABC = 90°.

Using a ruler and a pair of compasses only, construct:

A circle which passes through the points A, B and C and mark its centre as O.

Construct a triangle with sides 3 cm, 4 cm and 5 cm. Draw its circumcircle and measure its radius.

Using a ruler and compasses only:

Construct a triangle ABC with the following data: Base AB = 6 cm, AC = 5.2 cm and ∠CAB = 60°.

Using a ruler and compasses only:

In the same diagram, draw a circle which passes through the points A, B and C. and mark its centre O.

Using ruler and compasses only, draw an equilateral triangle of side 5 cm and draw its inscribed circle. Measure the radius of the circle.

Construct a triangle ABC with BC = 6.4 cm, CA = 5.8 cm and ∠ ABC = 60°. Draw its incircle. Measure and record the radius of the incircle.

Construct a ∆ABC with BC = 6.5 cm, AB = 5.5 cm, AC = 5 cm. Construct the incircle of the triangle. Measure and record the radius of the incircle.

The bisectors of angles A and B of a scalene triangle ABC meet at O.

What is the point O called?

The bisectors of angles A and B of a scalene triangle ABC meet at O.

OR and OQ is drawn a perpendicular to AB and CA respectively. What is the relation between OR and OQ?

The bisectors of angles A and B of a scalene triangle ABC meet at O.

What is the relation between ∠ACO and ∠BCO?

Using ruler and compasses only, construct a triangle ABC in which BC = 4 cm, ∠ACB = 45° and the perpendicular from A on BC is 2.5 cm. Draw the circumcircle of triangle ABC and measure its radius.

Construct a regular hexagon of side 4 cm. Construct a circle circumscribing the hexagon.

Draw a regular hexagon of side 4 cm and construct its incircle.