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

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## Chapter 19: Constructions (Circles)

Exercise 19

### Selina solutions for Concise Mathematics Class 10 ICSE Chapter 19 Constructions (Circles) Exercise 19 [Pages 292 - 293]

Exercise 19 | Q 1 | Page 292

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.

Exercise 19 | Q 2 | Page 292

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

Exercise 19 | Q 3 | Page 292

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

Exercise 19 | Q 4 | Page 292

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

Exercise 19 | Q 5 | Page 292

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.

Exercise 19 | Q 6 | Page 292

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

Exercise 19 | Q 7 | Page 292

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

Exercise 19 | Q 8 | Page 292

Using ruler and compasses only,
(i) Construct a triangle ABC with the following data:
Base AB = 6 cm, BC = 6.2 cm and ∠CAB = 60°
(ii) In the same diagram, draw a circle which passes through the points A, B and C and mark its center O.
(iii) draw a perpendicular from O to AB which meets AB in D.
(iv) Prove that AD = BD

Exercise 19 | Q 9 | Page 292

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

Exercise 19 | Q 10.1 | Page 293

Perpendicular bisectors of the sides AB and AC of a triangle ABC meet at O.
What do you call the point O?

Exercise 19 | Q 10.2 | Page 293

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?

Exercise 19 | Q 10.3 | Page 293

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

Does the perpendicular bisector of BC pass through O?

Exercise 19 | Q 11 | Page 293

The bisectors of angles A and B of a scalene triangle ABC meet at O.
(i) What is the point O called?
(ii) OR and OQ are drawn perpendicular to AB and CA respectively. What is the relation between OR and OQ?
(iii) What is the relation between angle ACO and angle BCO?

Exercise 19 | Q 12 | Page 293

(i) Using ruler and compasses only, construct a triangle ABC in which AB = 8 cm, BC = 6 cm
and CA = 5cm.
(ii) Find its in centre and mark it I.
(iii) 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.

Exercise 19 | Q 13 | Page 293

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

Exercise 19 | Q 14 | Page 293

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

Exercise 19 | Q 15 | Page 293

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

Exercise 19 | Q 16 | Page 293

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

Exercise 19 | Q 17 | Page 293

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

Exercise 19 | Q 18 | Page 293

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.

Exercise 19 | Q 19 | Page 293

Construct a triangle ABC in which base BC = 5.5 cm, AB = 6cm 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.

Exercise 19 | Q 20 | Page 293

Using a ruler and compasses only:

(1) construct a triangle ABC with the ffollowing data: AB=3.5cm,BC=6 cm and ∠ABC=120°.

(2) In the same diagram, draw a circle with BV as diameter. find a point P on the circumference of thge circle which is equidistant from AB and BC.

(3) Mesure ∠BCP

Exercise 19 | Q 21 | Page 293

Contruct a ΔABC with BC=6.5cm, AB=5.5 cm, AB=5.5 cm. construct the incircle of the triangle. Mesure and record the radius of the incricle.

Exercise 19 | Q 22 | Page 293

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 lemgth of PC

Exercise 19 | Q 23 | Page 293

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

Exercise 19 | Q 24 | Page 293

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.

Exercise 19 | Q 25 | Page 293

Using a ruler and a compass construct a triangle ABC in which AB = 7 cm, ∠CAB = 60o 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.

Exercise 19 | Q 26 | Page 293

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

Exercise 19 | Q 27 | Page 293

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.

Exercise 19 | Q 28 | Page 293

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.

Exercise 19

## Selina solutions for Concise Mathematics Class 10 ICSE chapter 19 - Constructions (Circles)

Selina solutions for Concise Mathematics Class 10 ICSE chapter 19 (Constructions (Circles)) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CISCE Concise Mathematics Class 10 ICSE solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Concise Mathematics Class 10 ICSE chapter 19 Constructions (Circles) are Circumscribing and Inscribing a Circle on a Regular Hexagon, Circumscribing and Inscribing a Circle on a Triangle, Construction of Tangents to a Circle, Circumscribing and Inscribing Circle on a Quadrilateral, Circumference of a Circle.

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