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Syllabus

In fig Op is equal to diameter of the circle. Prove that abp is a equilateral triangle..

sry abt the figure but i dnt know how to upload the figure

But its a circle with two tangents AP and BP... and joining OP, OA and OB ( o is the centre of the circle... )

Shivam has his hostel located at P and his school located at Q. Shivam drives his motorbike three day in a week and rides his car in the remaining 3 days,

to go to his school and back to hostel. POQ is a sector of a circle with centre O, central angle 60? and radius 4.2 km. Path POQ is the route for driving by motorbike and path PRO is for car only.

OPQR is a rhombus, three of whose vertices lie on a circle with centre O. If the area of the rhombus is 32 (under-root)3 cm

^{2}, find the radius of the circle.a motor cycle has diameter 91cm there are 22 spokes in the wheel find the length of the arc between the 2 adjoining spokes

The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is traveling at a speed of 66 km per hour?

please write in a simple method?

While doing dusting a maid found a button whose upper face is of black colour, as shown in the figure. The diameter of each of the smaller identical circles is 1/4 of the diameter of the larger circle whose radius is 16 cm.

Based on the above information, answer the following questions.

(i) The area of each of the smaller circle is

(a) 40.28 cm^{2}(b) 46.39 cm^{2}(c) 50.28 cm^{2}(d) 52.3 cm^{2}(ii) The area of the larger circle is

(a) 804.57 cm^{2}(b) 704.57 cm^{2}(c) 855.57 cm^{2}(d) 990.57 cm^{2}(iii) The area of the black colour region is

(a) 600.45 cm^{2}(b) 603.45 cm^{2}(c) 610.45 cm^{2}(d) 623.45 cm^{2}(iv) The area of quadrant of a smaller circle is

(a) 11.57 cm^{2}(b) 13.68 cm^{2}(c) 12 cm^{2}(d) 12.57 cm^{2}(v) If two concentric circles are of radii 2 cm and 5 cm, then the area between them is

(a) 60 cm^{2}(b) 63 cm^{2}(c) 66 cm^{2}(d) 68 cm^{2}PQRS is a diameter of a circle of radius 6cm. The lengths PQ, QR and RS are equal. Semi circles are drawn on PQ and QS as diameters. Find the perimeter and area of the region so obtained.

The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.

ABC is a right angled triangle, angle B=90* ,AB=28cm and BC=21cm. With AC as diameter a semicircle is drawn and with BC as radius a quarter cicle is drawn. Find the area of the shaded region

CASE STUDY BASED QUESTIONJohn had a farm with many animals like cows, dogs, horses etc. He had sufficient grass land for the cows and horses to graze. One day

three of his horses were tied with 7 m long ropes at the three corners of a triangular lawn having sides 20m, 34m and 42m.ANSWER THE FOLLOWING MCQs with Valid ExplanationsA. Area of the Triangular Lawn is:

- 326 m
- 336 m
- 306 m
- 316 m

B. Find the area that can be grazed by the horses.^{2}^{2}^{2}^{2}- 326 m
- 44 m
- 306 m
- 77 m

C. The cost of fencing the triangular lawn at the rate of Rs.30 per metre is:^{2}^{2}^{2}^{2}- Rs 2880
- Rs 2590
- Rs 10080
- Rs 3360

D. The area that cannot be grazed by the horses.- 326 m
- 259 m
- 336 m
- 316 m

E. John had a beautiful garden in the form of a quadrant of radius 7m. He wanted to fence it to protect the flowers. Find the length of wire required to fence it completely.^{2}^{2}^{2}^{2}Two circular flower beds have been shown on two sides of a square lawn ABCD of side 56 cm. If the centre of each circular flower bed is the point of intersection O of the diagonals of of the square lawn, find the sum of the areas of the lawn and flower beds.

In the given figure, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. [Use π = 3.14]

the long and short hands of a clock are 6cm and 4cm respectively.Find the sum of distances travelled by their tips in a day

Three circles of radius 2 cm touch one another externally. These circles are circumscribed by a circle of radius x. Find the value of x and the area of shaded region

ABCD is a trapezium with AB parallel to CD. AB=18cm, DC=32cm and distance between AB and DC=14cm. If arcs of equal radii 7cm with centres A,B,C and D have been drawn, then find the remaining area i.e. area exuding the circular region

The radius of a circle is 5 cm. A chord of length square root 50 cm is drawn in the circle. Find the area of the major segment.

Answer given in the book is 71.375 square cm

Whereas my calculation gives 71.428 sq cm

Kindly, check it?

The radius of a circle is 5 cm. A chord of length square root 50 cm is drawn in the circle. Find the area of the major segment.

Answer given in the book is 71.375 square cm

Whereas my calculation gives 71.428 sq cm

Kindly, check it?

AB=36 cm and M is the mid-point of AB. Semicircles are drawn on AB,AM and Mb as diametrs.A circle with centre C touches all the three circles. Find the area of the shaded region.

An elastic belt is placed round the rim of a pulley of radius 5 cm. One point on the belt is pulled directly away from the centre O of the pulley until it is at P, 10 cm from O.find the length of the belt that is in contact with the rim of the pulley.

in a circle of diameter 40 cm, a rhombus is inscribed with all its vertices on the circle. Find the area of rhombus

In the given figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.

two circles touch internally, the sum of their areas is 116 pie sq cm and distances between their centres is 6cm. find the radii of the circles.

plzzzzz ans!!!! its urgent!!!

The boundary of the shaded region in the figure given consists of four semi-circular arcs, the smallest two being equal. If the diameter of the larger is 14 cm and of the smallest is 3·5 cm, calculate the length of the boundary and the area of the shaded region. (Take = 22/7).

1] the perimeter of a quadrant of a circle of radius ' r ' is ___________.

2] Area of a quadrant of circle whose circomference is 22cm is ____________.

The area of the in-circle of an equilateral triangle side 42 cm is ?

in the fig O is the centre of circle with AC =24cm and AB=7 cm. and angle BOD =90. find the area of the shaded region..

NOT ABLE TO UPLOAD THE DIAGRAM....

its like a circle a diamete.two semicircles are thus formed.

one upper side of the diameter a triangleABC is formed with BC as its base n BC is the diameter...the on the lower side of the diameter the portion i.e the semicircle is biscetedby OD the radius...

IN the triangle AB is the smallest side AB the longest n AC the shortest...

pls make it as soon as possible tommorow is my maths exam...pls

aman has a tractor.the sum of the radii of two wheels of tractor is 98cm.and the diffrence of their circumference is 176cm.find the diameter of wheels.

In a circular table cover of radius 32 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in the given figure. Find the area of the design (Shaded region).

^{2}. Find the radius of each bead.A chord of a circle of radius 12 cm subtends an angle of 120° at the centre. Find the area of the corresponding segment of the circle. please explain me in easy way?

In figure, ABC is a right angled triangle, right angled at A. Semicircles are drawn on AB, AC and BC as diameters. Find the area of the shaded region.

Please see the figure:http://puu.sh/2e9qw

Acircular tablecloth of radius 30cm is to made .There should be two circular designed strips of width 5 cm each and width in between these strips is to be 5cm.. The radius of the inner circular plane portions is 10 cm. Find the total cost of making the two designed strips at the rate of Rs 0.75 per cm

^{2.}a wooden article was made by scooping out a hemisphere from each end of a solid cylinder.I the height of the cylinder is 10cm and it's base radius is 3.5cm. find it total s.a.

The perimeter of a semi-circular protractor is 72cm. Its diameter is :

(a)28cm

(b)14cm

(c)36cm

(d)24cm

Find the area of the shaded region in the given figure, where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre.

CASE STUDY BASED QUESTIONJohn had a farm with many animals like cows, dogs, horses etc. he had sufficient grass land for the cows and horses to graze. One day THREE of his horses were tied with 7 m long ropes at the three corners of a triangular lawn having sides 20m, 34 m and 42m.

Answer the following MCQs with VALID EXPLANATIONS (AREAS RELATED TO CIRCLES)A. The Area that cannot be grazed by horses

- 326 m
- 259 m
- 336 m
- 316 m

B.John had a beautiful garden in the form of a quadrant of radius 7m. He wanted to fence it to protect the flowers. Find the length of the wire required to fence it completely.^{2}^{2}^{2}^{2}M

pls explain me

a) 4 p cm b) 6 p cm c) 7 p cm d) 8 p cm

The area of a circle inscribed in an equilateral triangle is 154 cm2. Find the perimeter of the triangle.

Find the diameter of circle whose area is 301.84 cm

^{2 }?The inner circumference of the circular track is 440 m and the track is 14 m wide.Calculate the cost of levelling the track at the rate of 25 paise per sq. m.Also, find the cost of fencing the outer circle at the of Rs. 5 per m.[Use pi = 22/7]

In an equilateral triangle of side 24cm , a circle is inscribed touching its sides . Find the area of the remaining portion of the triangle .

in a figure,a circle is inscribed in a square of side 4cm and another ciccle is circumscribing the square.Proove that the area of the circumscribed ciccle is two times the area of the inscribed circle.

please i want the answer too fast!its an emergency.

Fig shows a sector of a circle, centre O containing an angle θ.

Find the perimeter and area of the shaded region.

find i) perimeter = r (tan θ + sec θ + πθ/180 – 1)

ii)Area = r2/2(tan θ – πθ /180)

i need fully solved ..........hurry please....

an archery target has 3 regions formed by three concentric circles. if the diameters of the concentric circles are in the ratio 1:2:3, then find the ratio of the areas of the regions???guys plz help me....

need this answer before 10:30 am today...

2.If the area and circumference of a circle are numerically equal, then its radius is

3.The length of a rectangular field is 23 m more than its breadth. If the perimeter of the field is

4.The area of a sector of a circle with radius r, making an angle of x° at the centre is

5.If O is a fixed point and Q is a point which moves in such a way that the distance OQ remains constant, then the locus of Q is called

Find the area of a quadrant of a circle whose circumference is 22cm.

The question for the answer is: In a circular table of radius 32 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in the given figure. Find the area of the design(shaded region)

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

all the vertices of a rhombus lie on a circle. find the area of the rhombus if the area of the circle is 1256cm

^{2}## A sector is cut from a circular sheet of radius100cm, the angle of the sector being240∘. If another circle of the area same as the sector is formed, then radius of the new circle is

a bicycle wheel makes 5000 revolutions in moving 11km find diameter of the wheel

a)the circumference of the central part

b)the perimeter of the part ABEF

Q=AB is the diameter of a circle,center O .C is a point on the circumference such that /-COB=a.The area of minor segment cut off by AC is equal to twice the area of the sector BOC. Prove thatsin a/2 cos a/2 =pie(1/2- a/120)The radii of the front and rear wheels of a tractor are 42cm and 70cm respectively. Find the number of revolution r that the rear will make in covering a distance,in which the fron wheel makes 66o revolution

With vertices A,B and C of a triangle ABC as centres, arcs are drawn with 5cm each. With sides AB=14cm, BC=48cm and CA =50cm, find Area of whole triangle minus the sum of the three sectors

The diagram shows a right angled triangle and a semi circle. PQ is the diameter of the semicircle. The perimeter of the whole diagam is... (a) 30 + 5pi (b)18 +6pi (c) 18 + 10pi

ABCD is a trapezium AB ||DC and angle BCD =60 degree.if befc is sector with center C and ab=bc=7cm and de=4 cm ,then find the area of the shaded region?

Two Concentric Circles of radii A and B ( A>B) are given. the Chord AB of larger circle touches the smaller circle at C. The length of AB is

If the angle between two radii of a circle is 100 degree, the angle between the tangents at the ends of those radii is

If a, b and c are the sides of a right angle triangle where C is the hypotenuse. Prove that radius, r of the circle touches the sides of the triangle given by

r=a+b-c21. the shape of the top of a table in a restaurant is that of a sector of a circle with centre O an dang;e bod=90. if bo=od=60cm, find the area of the table and the perimeter of the table top.

2. triangle ABC is right angled at A. semicircles are drawn on AB, AC and BC as diameters. find the area of the shaded region .

3.OPQR is a rhombus , three of whose vertices lie on a circle with centre O. if the area of the rhombus is 32root3 cm sq. , find the radius of the circle.

4.O is the centre of the biggre circle an dAC is the diameter. another circle with AB as diameter is drawn. if AC=54cm and BC=10cm, find the area of the shaded region.

2.The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36cm and 20cm is

3.If the area of a sector of a circle is of the area of the circle is 7/20 then the sector angle is equal to

4.If the radius of a circle is diminished by 10%, then its area is diminished by

5.The area of an equilateral triangle is 4 underoot 3 cm2 . Its perimeter is?

ABCP is a quadrant of a circle of radius 14 cm With AC as a diameter, a semicircle is drawn. Find the area of the shaded region. (Take Pi=22/7)

The figure consists of a rt. angled triangle ABC, with AC as the hypotenuse. A semicircle APC is drawn with AC as the diameter. Over this, another the arc of the quadrant extends. The shaded region is between the arc of the semicircle and the arc of the quadrant.

Relation between the area of sector and the length of an arc:Look at the following figure.Here, O is the centre of the circle of radius

rand APB is an arc of lengthl.Clearly, measure of arc APB = Central angle =

θLet the area of sector OAPB be A.

Now, we have

From length of arc and area of corresponding sector, we can also conclude that.

here i understood the first part very clearly i.e. till area of setor=radius/2*length of arc

but i am not able to understand the second relation.

pls help me in understanding it.

what is the formula of area of minor segment and major segment?

An arc of a circle is of length 5pi cm and the sector it bounds an area of 20pi cm

^{2}. find the radius of the circleThe area of an equilateral triangle ABC is 17320.5 cm

^{2}. With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle (See the given figure). Find the area of shaded region. [Use π = 3.14 and]plz answer this question....and plz tell me step by step......can anyone...help me..

in a circle with centre o.the area of sector oAPB is 5/18 of the area find the area of x

an equilateral triangle abc of side 6 cm has been inscribed in a circle . find the area of the shaded region . thai is the remaining part of the circle

In RD Sharma Chapter 15 : Areas related to circles: Revision exercise Question 32, how is the radius of the circle with centre C ,1/6th of AB ..???

2.The parallel sides of a trapezium are 9.7 cm and 6.3 cm, and the distance between them is 6.5 cm. The area of the trapezium is

3.The ratio of the areas of a circle and an equilateral triangle whose diameter and a side are respectively equal, is

4.The circumference of a circle is 100 cm. The side of a square inscribed in the circle is

5.The hour hand of a clock is 6 cm long. The area swept by it between 11.20 am and 11.55 am is

3 circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two . find the area enclosed between these three cicles (shaded region )use pie=22/7?