#### Chapters

## Chapter 6: Circle

#### Practice Set 6.1 [Page 79]

### Balbharati solutions for Maharashtra state board SSC 9th Standard Maths 2 Geometry Chapter 6 Circle Practice Set 6.1 [Page 79]

Distance of chord AB from the centre of a circle is 8 cm. Length of the chord AB is 12 cm. Find the diameter of the circle.

Diameter of a circle is 26 cm and length of a chord of the circle is 24 cm. Find the distance of the chord from the centre.

Radius of a circle is 34 cm and the distance of the chord from the centre is 30 cm, find the length of the chord.

Radius of a circle with centre O is 41 units. Length of a chord PQ is 80 units, find the distance of the chord from the centre of the circle.

In the given figure, centre of two circles is O. Chord AB of bigger circle intersects the smaller circle in points P and Q. Show that AP = BQ

Prove that, if a diameter of a circle bisects two chords of the circle then those two chords are parallel to each other.

#### Practice Set 6.2 [Page 82]

### Balbharati solutions for Maharashtra state board SSC 9th Standard Maths 2 Geometry Chapter 6 Circle Practice Set 6.2 [Page 82]

Radius of circle is 10 cm. There are two chords of length 16 cm each. What will be the distance of these chords from the centre of the circle ?

In a circle with radius 13 cm, two equal chords are at a distance of 5 cm from the centre. Find the lengths of the chords.

Seg PM and seg PN are congruent chords of a circle with centre C. Show that the ray PC is the bisector of ∠ NPM.

#### Practice Set 6.3 [Page 86]

### Balbharati solutions for Maharashtra state board SSC 9th Standard Maths 2 Geometry Chapter 6 Circle Practice Set 6.3 [Page 86]

Construct Δ ABC such that ∠B = 100° , BC = 6.4 cm, ∠C = 50° and construct its incircle.

Construct Δ PQR such that ∠P = 70° , ∠R = 50° , QR = 7.3 cm and constructs its circumcircle.

Construct Δ XYZ such that XY = 6.7 cm ,YZ = 5.8 cm, XZ = 6.9 cm and constructs its incircle.

In Δ LMN, LM = 7.2 cm, ∠M = 105° , MN = 6.4 cm , then draw Δ LMN and construct its circumcircle.

Construct Δ DEF such that DE = EF = 6 cm, ∠ F = 45° and constructs its circumcircle.

#### Problem Set 6, Problem Set 6 [Pages 86 - 87]

### Balbharati solutions for Maharashtra state board SSC 9th Standard Maths 2 Geometry Chapter 6 Circle Problem Set 6, Problem Set 6 [Pages 86 - 87]

Choose correct alternative answer and fill in the blank.

Radius of a circle is 10 cm and distance of a chord from the centre is 6 cm. Hence the length of the chord is .........

16 cm

8 cm

12 cm

32 cm

Choose correct alternative answer and fill in the blank.

The point of concurrence of all angle bisectors of a triangle is called the ......

centroid

circumcentre

incentre

orthocentre

Choose correct alternative answer and fill in the blank.

The circle which passes through all the vertices of a triangle is called .....

circumcircle

incircle

congruent circle

concentric circle

Choose correct alternative answer and fill in the blank.

Length of a chord of a circle is 24 cm. If distance of the chord from the centre is 5 cm, then the radius of that circle is ....

12 cm

13 cm

14 cm

15 cm

Choose correct alternative answer and fill in the blank.

The length of the longest chord of the circle with radius 2.9 cm is .....

3.5 cm

7 cm

10 cm

5.8 cm

Choose correct alternative answer and fill in the blank.

Radius of a circle with centre O is 4 cm. If l(OP) = 4.2 cm, say where point P will lie.

on the centre

Inside the circle

outside the circle

on the circle

Choose correct alternative answer and fill in the blank.

The lengths of parallel chords which are on opposite sides of the centre of a circle are 6 cm and 8 cm. If radius of the circle is 5 cm, then the distance between these chords is .....

2 cm

1 cm

8 cm

7 cm

Construct incircle and circumcircle of an equilateral

Δ DSP with side 7.5 cm. Measure the radii of both the circles and find the ratio of radius of circumcircle to the radius of incircle.

Construct Δ NTS where NT = 5.7 cm, TS = 7.5 cm and

∠ NTS = 110 ° and draw incircle and circumcircle of it.

In the given figure, C is the centre of the circle. seg QT is a diameter CT = 13, CP = 5, find the length of chord RS.

In the given figure, CD is a diameter of the circle with centre O. Diameter CD is perpendicular to chord AB at point E. Show that Δ ABC is an isosceles triangle.

## Chapter 6: Circle

## Balbharati solutions for Maharashtra state board SSC 9th Standard Maths 2 Geometry chapter 6 - Circle

Balbharati solutions for Maharashtra state board SSC 9th Standard Maths 2 Geometry chapter 6 (Circle) 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 Maharashtra State Board Maharashtra state board SSC 9th Standard Maths 2 Geometry solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Maharashtra state board SSC 9th Standard Maths 2 Geometry chapter 6 Circle are Concept of Circles, Properties of Chord, Incircle Of a triangle, Circumcircle of circle.

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