#### Chapters

Chapter 2 - Banking (Recurring Deposit Account)

Chapter 3 - Shares and Dividend

Chapter 4 - Linear Inequations (In one variable)

Chapter 5 - Quadratic Equations

Chapter 6 - Solving (simple) Problems (Based on Quadratic Equations)

Chapter 7 - Ratio and Proportion (Including Properties and Uses)

Chapter 8 - Remainder and Factor Theorems

Chapter 9 - Matrices

Chapter 10 - Arithmetic Progression

Chapter 11 - Geometric Progression

Chapter 12 - Reflection

Chapter 13 - Section and Mid-Point Formula

Chapter 14 - Equation of a Line

Chapter 15 - Similarity (With Applications to Maps and Models)

Chapter 16 - Loci (Locus and Its Constructions)

Chapter 17 - Circles

Chapter 18 - Tangents and Intersecting Chords

Chapter 19 - Constructions (Circles)

Chapter 20 - Cylinder, Cone and Sphere

Chapter 21 - Trigonometrical Identities

Chapter 22 - Height and Distances

Chapter 23 - Graphical Representation

Chapter 24 - Measure of Central Tendency(Mean, Median, Quartiles and Mode)

Chapter 25 - Probability

## Chapter 19 - Constructions (Circles)

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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°.

(i) Construct a circle circumscribing the triangle ABC.

(ii) draw a cyclic quadrilateral ABCD so that D is equidistant from B and C.