Nootan solutions for Mathematics [English] Class 10 ICSE chapter 16 - Constructions [Latest edition]

Draw a circle of radius 5 cm. Mark a point P outside the circle at a distance of 7 cm from the centre. Construct two tangents from P to the circle. Measure and write down the length of one tangent.

Draw a circle of radius 3.5 cm. Mark a point P outside the circle at a distance of 5 cm from the centre. Construct two tangents from P to the given circle. Measure and write down the length of one tangent.

Draw a circle of radius 6 cm. Mark a point at a distance of 9 cm from the centre. Construct two tangents to the circle from this point. Measure the length of each tangent.

Use ruler and compass only for answering this question.

Draw a circle of radius 4 cm. Mark the centre as O. Mark a point P outside the circle at a distance of 7 cm from the centre. Construct two tangents to the circle from the external point P.

Measure and write down the length of any one tangent.

Construct a ΔABC in which ∠A = 90°, AB = 6 cm and AC = 4.5 cm. Bisect AC at O. Draw a circle with centre O and radius ОС. Draw two tangents to this circle from point B.

Using ruler and compasses, draw a ΔABC in which BC = 7 cm, CA = 5 cm, and AB = 6 cm and construct its circumcircle. Also write the steps of construction.

Construct the circumcircle of the ΔABC when AB = 5 cm, BC = 7 cm and ∠ABC = 50°.

Draw an equilateral Δ of sides 5 cm. Draw the circumcircle of it.

Draw a triangle whose sides are 6 cm, 5 cm and 6 cm and inscribe a circle in it. Find by measurement its radius.

Draw an isosceles triangle with sides 6 cm, 4 cm, and 6 cm. Construct the incircle of the triangle. Also, write the steps of construction.

Draw a right angled triangle ABC with AB = 4.5 cm, AC = 7.5 cm and ∠B = 90°. Construct the incircle. Write the steps of construction also.

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

Draw a regular hexagon of side 3.5 cm. Construct a circle circumscribing the regular hexagon.

Draw a regular hexagon of side 3.6 cm. Construct a circle inscribing the regular hexagon.

Draw a regular hexagon of side 4.2 cm. Construct a circle inscribing the regular hexagon.

Using ruler and compass construct a triangle ABC in which AB = 6 cm, ∠BAC = 120° and AC = 5 cm. Construct a circle passing through A, B and C. Measure and write down the radius of the circle.

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

Using ruler and compass only, construct a ΔABC such that BC = 5 cm and AB = 6.5 cm and ∠ABC = 120°

1. Construct a circumcircle of ΔABC
2. Construct a cyclic quadrilateral ABCD, such that D is equidistant from AB and BC.

Contruct a ΔABC 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 incricle.

Construct a regular hexagon of side 3.4 cm. Construct a circle circumscribing it.

Construct a regular hexagon of side 3.8 cm. Construct a circle inscribing it.

Draw a line AB = 5 cm. Mark a point C on AB such that AC = 3 cm. Using a ruler and a compass only, construct:

1. A circle of radius 2.5 cm, passing through A and C.
2. Construct two tangents to the circle from the external point B. Measure and record the length of the tangents.

Draw a circle of radius 3 cm. Form a point P, 7 cm away from the centre of the circle, draw two tangents to the circle. Also, measure the lengths 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.