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

## Chapter 19: Constructions (Circles)

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#### Chapter 19: Constructions (Circles) Exercise 19A solutions [Page 0]

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,
(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.

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,
(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

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.

Perpendicular bisectors of the sides AB and AC of a triangle ABC meet at O.
(i) What do you call the point O?
(ii) what is the relation between the distances OA, OB and OC?
(iii) Does the perpendicular bisector of BC pass through O?

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?

(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.

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 = 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.

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

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.

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

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

Selina solutions for Class 10 Maths 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 Selina ICSE Concise Mathematics for Class 10 (2018-2019) solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com are providing such solutions so that students can prepare for written exams. Selina textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 10 Mathematics 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.

Using Selina Class 10 solutions Constructions (Circles) exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Selina Solutions are important questions that can be asked in the final exam. Maximum students of CISCE Class 10 prefer Selina Textbook Solutions to score more in exam.

Get the free view of chapter 19 Constructions (Circles) Class 10 extra questions for Maths and can use Shaalaa.com to keep it handy for your exam preparation

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