Selina solutions for Mathematics [English] Class 10 ICSE chapter 19 - Constructions (Circles) [Latest edition]

Draw a circle of radius 3 cm. Mark a point P at a distance of 5 cm from the centre of the circle drawn. Draw two tangents PA and PB to the given circle and measure the length of each tangent. 

Draw a circle of diameter 9 cm. Mark a point at a distance of 7.5 cm from the centre of the circle. Draw tangents to the given circle from this exterior point. Measure the length of each tangent.

Draw a circle of radius 5 cm. Draw two tangents to this circle so that the angle between the tangents is 45°.

Draw a circle of radius 4.5 cm. Draw two tangents to this circle so that the angle between the tangents is 60°.  

Using ruler and compasses only, draw an equilateral triangle of side 4.5 cm and draw its circumscribed circle. Measure the radius of the circle.  

Using ruler and compasses only,

1. Construct triangle ABC, having given BC = 7 cm, AB – AC = 1 cm and ∠ABC = 45°.
2. Inscribe a circle in the ΔABC constructed in (i) above. Measure its radius.

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

Using ruler and compasses only,

1. Construct a triangle ABC with the following data :
   Base AB = 6 cm, BC = 6.2 cm and ∠CAB = 60°.
2. In the same diagram, draw a circle which passes through the points A, B and C and mark its center O.
3. Draw a perpendicular from O to AB which meets AB in D.
4. Prove that : AD = BD.

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.  

Perpendicular bisectors of the sides AB and AC of a triangle ABC meet at O.

1. What do you call the point O?
2. What is the relation between the distances OA, OB and OC?
3. Does the perpendicular bisector of BC pass through O?

Perpendicular bisectors of the sides AB and AC of a triangle ABC meet at O.

What is the relation between the distances OA, OB and OC?

Perpendicular bisectors of the sides AB and AC of a triangle ABC meet at O. 

Does the perpendicular bisector of BC pass through O? 

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

1. What is the point O called?
2. OR and OQ are drawn perpendicular to AB and CA respectively. What is the relation between OR and OQ?
3. What is the relation between angle ACO and angle BCO?

1. Using ruler and compasses only, construct a triangle ABC in which AB = 8 cm, BC = 6 cm and CA = 5 cm.
2. Find its in centre and mark it I.
3. With I as centre, draw a circle which will cut off 2 cm chords from each side of the triangle. What is the length of the radius of this circle. 

Construct an equilateral triangle ABC with side 6 cm. Draw a circle circumscribing the triangle ABC. 

Construct a circle, inscribing an equilateral triangle with side 5.6 cm. 

Draw a circle circumscribing a regular hexagon with side 5 cm. 

Draw an inscribing circle of a regular hexagon of side 5.8 cm.

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

Draw a circle of radius 3.5 cm. Mark a point P outside the circle at a distance of 6 cm from the centre. Construct two tangents from P to the given circle. Measure and write down the length of one tangent. 

Construct a triangle ABC in which base BC = 5.5 cm, AB = 6 cm and ∠ABC = 120°.

1. Construct a circle circumscribing the triangle ABC.
2. Draw a cyclic quadrilateral ABCD so that D is equidistant from B and C. 

Using a ruler and compasses only: 

1. Construct a triangle ABC with the following data: AB = 3.5 cm, BC = 6 cm and ∠ABC = 120°.
2. In the same diagram, draw a circle with BC as diameter. Find a point P on the circumference of the circle which is equidistant from AB and BC. 
3. Measure ∠BCP.

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.

Constuct a triangle ABC with AB = 5.5 cm, AC = 6 cm and ∠BAC = 105°. Hence: 

1. Construct the locus of point equdistant from BA and BC.
2. Construct the locus of points equidistant from B and C.
3. Mark the point which satisfies the above two loci as P. Measure and write the length of PC.

Construct a regular hexagon of side 5 cm. Hence construct all its lines of symmetry and name them.

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.

Using a ruler and a compass, construct a triangle ABC in which AB = 7 cm, ∠CAB = 60° and AC = 5 cm. Construct the locus of :

1. points equidistant from AB and AC.
2. points equidistant from BA and BC.
   Hence construct a circle touching the three sides of the triangle internally.

Construct a triangle ABC in which AB = 5 cm, BC = 6.8 cm and median AD = 4.4 cm. Draw incircle of this triangle.

Draw two concentric circles with radii 4 cm and 6 cm. Taking a point on the outer circle, construct a pair of tangents to inner circle. By measuring the lengths of both the tangents, show that they are equal to each other.

In triangle ABC, ∠ABC = 90°, AB = 6 cm, BC = 7.2 cm and BD is perpendicular to side AC. Draw circumcircle of triangle BDC and then state the length of the radius of this circumcircle drawn.