R d sharma solutions mathematics class 9 Solutions for Chapter 16 circles

Exercises in Chapter 16 circles Grade 9

Circles Exercise 16.1

Circles Exercise 16.2

Circles Exercise 16.3

Circles Exercise 16.4

Circles Exercise 16.5

Questions in Circles Exercise 16.1

Fill in the blanks:

(i) All points lying inside/outside a circle are called___ points/ points.

(ii) Circles having the same centre and different radii are called_ circles.

(iii) A point whose distance from the center of a circle is greater than its radiuslies in_ of the circle.

(iv) A continuous piece of a circle is_ of the circle.

(v) The longest chord of a circle is a _____of the circle.

(vi) An arc is a_ when its ends are the ends of a diameter.

(vii) Segment of a circle is a region between an arc and _____of the circle.

(viii) A circle divides the plane, on which itlies, in _____parts.

Questions in Circles Exercise 16.2

Find the length of a chord which is at a distance of 5 cm from the centre of a circle of radius 10 cm.

Prove that the line joining the mid-point of a chord to the centre of the circle passes through the mid-point of the corresponding minor arc.

Questions in Circles Exercise 16.3

A circular park of radius 40 m is situated in a colony. Three boys Ankur, Amit and Anand are sitting at equal distance on its boundary each having a toy telephone in his hands to talk to each other. Find the length of the string of each phone.

Questions in Circles Exercise 16.4

In figure, O is the centre of the circle. Find ∠BAC.

If O is the centre of the circle, find the value of x in each of the following figures.

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

(xi)

(xii)

O is the circumcentre of the triangle ABC and OD is perpendicular on BC. Prove that ∠BOD = ∠A

In figure, O is the centre of the circle, BO is the bisector of ∠ABC. Show that AB = AC [[> widget id="1" <]

In figure, O is the centre of the circle, then prove that ∠x = ∠y + ∠z

Questions in Circles Exercise 16.5

If ABCD is a cyclic quadrilateral in which AD||BC (figure). Prove that ∠B = ∠C.

In figure, O is the centre of the circle. Find ∠CBD

In figure, AB and CD are diameters of a circle with centre O. If ∠OBD = $50^0$ find ∠AOC.

In a cyclic quadrilateral ABCD if AB||CD and B = $70^0$ , find the remaining angles.

In a cyclic quadrilateral ABCD, if m ∠A = 3(m∠C). Find m ∠A.

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Chapters in this book

Number System

Exponents Of Real Numbers

Rationalisation

Algebraic Identities

Factorization Of Algebraic Expressions

Factorization Of Polynomials

Introduction To Euclid’s Geometry

Lines And Angles

Triangle And Its Angles

Congruent Triangles

Coordinate Geometry

Herons Formula

Linear Equations In Two Variables

Quadrilaterals

Areas Of Parallelograms And Triangles

Circles

Constructions

Surface Area And Volume Of A Cuboid And Cube

Surface Area And Volume Of a Right Circular Cylinder

Surface Area And Volume Of a Right Circular Cone

Surface Area And Volume Of Sphere

Tabular Representation Of Statistical Data

Graphical Representation Of Statistical Data

Measures Of Central Tendency

Probability