#### Chapters

Chapter 2 - Polynomials

Chapter 3 - Pair of Linear Equations in Two Variables

Chapter 4 - Triangles

Chapter 5 - Trigonometric Ratios

Chapter 6 - Trigonometric Identities

Chapter 7 - Statistics

Chapter 8 - Quadratic Equations

Chapter 9 - Arithmetic Progression

Chapter 10 - Circles

Chapter 11 - Constructions

Chapter 12 - Trigonometry

Chapter 13 - Probability

Chapter 14 - Co-Ordinate Geometry

Chapter 15 - Areas Related to Circles

Chapter 16 - Surface Areas and Volumes

## Chapter 15 - Areas Related to Circles

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Find the circumference and area of circle of radius 4.2 cm

Fill in the blank:

The common point of a tangent to a circle and the circle is called ____

Fill in the blank:

A circle can have __________ parallel tangents at the most.

Fill in the blank:

A tangent to a circle intersects it in _______ point (s).

Fill in the blank:

A line intersecting a circle in two points is called a __________.

Find the circumference of a circle whose area is 301.84 cm^{2}.

How many tangents can a circle have?

Find the area of circle whose circumference is 44 cm.

The circumference of a circle exceeds diameter by 16.8 cm. Find the circumference of

circle.

A horse is tied to a pole with 28m long string. Find the area where the horse can graze.

A steel wire when bent is the form of square encloses an area of 12 cm2. If the same wire is bent in form of circle. Find the area of circle.

A horse is placed for grazing inside a rectangular field 40m by 36m and is tethered to one corner by a rope 14m long. Over how much area can it graze.

A sheet of paper is in the form of rectangle ABCD in which AB = 40cm and AD = 28 cm. A semicircular portion with BC as diameter is cut off. Find the area of remaining paper.

The circumference of two circles are in ratio 2:3. Find the ratio of their areas

The side of a square is 10 cm. find the area of circumscribed and inscribed circles.

The sum of the radii of two circles is 140 cm and the difference of their circumferences in 88 cm. Find the diameters of the circles.

The area of circle, inscribed in equilateral triangle is 154 cms2. Find the perimeter of

triangle.

A field is in the form of circle. A fence is to be erected around the field. The cost of fencing would to Rs. 2640 at rate of Rs.12 per metre. Then the field is to be thoroughs ploughed at cost of Rs. 0.50 per m2. What is amount required to plough the field?

If a square is inscribed in a circle, find the ratio of areas of the circle and the square.

A park is in the form of rectangle 120m × 100m. At the centre of park there is a circular lawn. The area of park excluding lawn is 8700m2. Find the radius of circular lawn.

The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles.

The radii of two circles are 19cm and 9 cm respectively. Find the radius and area of the circle which has circumferences is equal to sum of circumference of two circles.

A car travels 1 km distance in which each wheel makes 450 complete revolutions. Find the radius of wheel.

The area enclosed between the concentric circles is 770cm2. If the radius of outer circle 21cm. find the radius of inner circle

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Find in terms of x the length of the arc that subtends an angle of 30°, at the centre of circle of radius 4 cm.

Find the angle subtended at the centre of circle of radius 5cm by an arc of length `((5pi)/3)` cm

An arc of length 20𝜋 cm subtends an angle of 144° at centre of circle. Find the radius of the circle.

An arc of length 15 cm subtends an angle of 45° at the centre of a circle. Find in terms of 𝜋, radius of the circle.

Find the angle subtended at the centre of circle of radius ‘a’ cm by an arc of length

`(api)/4` 𝑐𝑚

A sector of circle of radius 4cm contains an angle of 30°. Find the area of sector

A sector of a circle of radius 8cm contains the angle of 135°. Find the area of sector.

The area of sector of circle of radius 2cm is 𝜋cm2. Find the angle contained by the sector.

The area of sector of circle of radius 5cm is 5𝜋 cm2. Find the angle contained by the sector.

AB is a chord of circle with centre O and radius 4cm. AB is length of 4cm. Find the area of sector of the circle formed by chord AB

In a circle of radius 35 cm, an arc subtends an angle of 72° at the centre. Find the length of arc and area of sector

The perimeter of a sector of circle of radius 5.7m is 27.2 m. Find the area of sector.

The perimeter of certain sector of circle of radius 5.6 m is 27.2 m. Find the area of sector.

A sector is cut-off from a circle of radius 21 cm the angle of sector is 120°. Find the length of its arc and its area.

The minute hand of a clock is √21 𝑐𝑚 long. Find area described by the minute hand on the face of clock between 7 am and 7:05 am

The minute hand of clock is10cm long. Find the area of the face of the clock described by the minute hand between 8am and 8:25 am

Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre

A sector of 56° cut out from a circle contains area of 4.4 cm2. Find the radius of the circle

In circle of radius 6cm, chord of length 10 cm makes an angle of 110° at the centre of circle find Circumference of the circle

In circle of radius 6cm, chord of length 10 cm makes an angle of 110° at the centre of circle find Area of the circle

In circle of radius 6cm, chord of length 10 cm makes an angle of 110° at the centre of circle find Length of arc

In circle of radius 6cm, chord of length 10 cm makes an angle of 110° at the centre of circle find The area of sector

Below fig shows a sector of a circle, centre O. containing an angle 𝜃°. Prove that Perimeter of shaded region is 𝑟 (tan 𝜃 + sec 𝜃 +`(pitheta)/180`− 1)

Below fig shows a sector of a circle, centre O. containing an angle 𝜃°. Prove that

Area of shaded region is`r^2/2(tantheta −(pitheta)/180)`

The diagram shows a sector of circle of radius ‘r’ can containing an angle 𝜃. The area of sector is A cm2 and perimeter of sector is 50 cm. Prove that

(i) 𝜃 =`360/pi(25/r− 1)`

(ii) A = 25r – r^{2}

In Fig. 7, two equal circles, with centres O and O’, touch each other at X. OO’ produced meets the circle with centre O’ at A. AC is tangent to the circle with centre O, at the point C. O’D is perpendicular to AC. Find the value of `(DO')/(CO')`

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AB is a chord of a circle with centre O and radius 4 cm. AB is of length 4 cm and divides the circle into two segments. Find the area of the minor segment.

A chord of circle of radius 14cm makes a right angle at the centre. Find the areas of minor and major segments of the circle.

A chord 10 cm long is drawn in a circle whose radius is 5√2 cm. Find the area of both

segments

A chord AB of circle, of radius 14cm makes an angle of 60° at the centre. Find the area of minor segment of circle.

AB is the diameter of a circle, centre O. C is a point on the circumference such that ∠COB = 𝜃. The area of the minor segment cutoff by AC is equal to twice the area of sector BOC.Prove that `"sin"theta/2. "cos"theta/2= pi (1/2−theta/120^@)`

A chord of a circle subtends an angle 𝜃 at the centre of circle. The area of the minor segment cut off by the chord is one eighth of the area of circle. Prove that 8 sin`theta/2 "cos"theta/2+pi =(pitheta)/45`

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A plot is in the form of rectangle ABCD having semi-circle on BC. If AB = 60m and BC = 28m, find the area of plot.

A playground has the shape of rectangle, with two semicircles on its smaller sides as

diameters, added to its outside. If the sides of rectangle are 36m and 24.5m. find the area of playground.

The outer circumference of a circular race track is 528m. The track is everywhere 14m

wide. Calculate the cost of leveling the track at rate of 50 paise per square metre.

A rectangular piece is 20m long and 15m wide from its four corners, quadrants of 3.5m radius have been cut. Find the area of remaining part.

Four equal circles, each of radius 5 cm touch each other as shown in fig. Find the area

included between them.

Four cows are tethered at four corners of a square plot of side 50m, so that’ they just cant reach one another. What area will be left ungrazed.

A road which is 7m wide surrounds a circular park whose circumference is 352m. Find the area of road.

Four equal circles each of radius a, touch each other. Show that area between them is `6/7a^2`

A square water tank has its side equal to 40m, there are 4 semicircular flower beds grassy plots all around it. Find the cost of turfing the plot at Rs 1.25/sq.m

#### Textbook solutions for Class 10

## R.D. Sharma solutions for Class 10 Mathematics chapter 15 - Areas Related to Circles

R.D. Sharma solutions for Class 10 Mathematics chapter 15 (Areas Related to Circles) include all questions with solution and detail explanation from 10 Mathematics. 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 created the CBSE 10 Mathematics solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 10 Mathematics chapter 15 Areas Related to Circles are Areas of Combinations of Plane Figures, Areas of Sector and Segment of a Circle, Perimeter and Area of a Circle, Problems Based on Areas and Perimeter Or Circumference of Circle, Sector and Segment of a Circle, Areas Related to Circles Examples and Solutions, Tangents and Its Properties, Tangent to a Circle, Number of Tangents from a Point on a Circle, Touching Circles, Introduction to an Arc, Angle Subtended by the Arc to the Centre, Angle Subtended by the Arc to the Point on the Circle, Cyclic Quadrilateral, Tangent - Secant Theorem, Cyclic Properties, Tangent Properties - If Two Circles Touch, the Point of Contact Lies on the Straight Line Joining Their Centers, Theorem - Converse of Tangent at Any Point to the Circle is Perpendicular to the Radius, Number of Tangents from a Point to a Circle.

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