CBSE Class 10 Mathematics Circles Worksheet Set B

Read and download free pdf of CBSE Class 10 Mathematics Circles Worksheet Set B. Download printable Mathematics Class 10 Worksheets in pdf format, CBSE Class 10 Mathematics Chapter 10 Circles Worksheet has been prepared as per the latest syllabus and exam pattern issued by CBSE, NCERT and KVS. Also download free pdf Mathematics Class 10 Assignments and practice them daily to get better marks in tests and exams for Class 10. Free chapter wise worksheets with answers have been designed by Class 10 teachers as per latest examination pattern

Chapter 10 Circles Mathematics Worksheet for Class 10

Class 10 Mathematics students should refer to the following printable worksheet in Pdf in Class 10. This test paper with questions and solutions for Class 10 Mathematics will be very useful for tests and exams and help you to score better marks

Class 10 Mathematics Chapter 10 Circles Worksheet Pdf

 

Q.-  Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
 
Sol. Given : CD and EF are the tangents at the end points A and B of the diameter AB of a circle with centre O.
To prove : CD || EF.
Circles notes 3
 
Proof : CD is the tangent to the circle at the point A.
∴ ∠BAD = 90°
EF is the tangent to the circle at the point B.
∴ ∠ABE = 90°
Thus, BAD = ABE (each equal to 90°).
But these are alternate interior angles.
 CD || EF
 
Q.- Prove that the line segment joining the point of contact of two parallel tangents to a circle is a diameter of the circle.
 
Sol. Given : CD and EF are two parallel tangents at the points A and B of a circle with centre O.
Circles notes 4
To prove : AOB is a diameter of the circle.
Construction : Join OA and OB.
Draw OG || CD
Proof : OG || CD and AO cuts them.
∴ ∠CAO + GOA = 180°
=> 90°+GOA = 180° [OA⊥CD]
=> GOA = 90°
Similarly,  GOB = 90°
∴ GOA + GOB = (90° + 90°) = 180° 
=> AOB is a straight line
Hence, AOB is a diameter of the circle with centre O.
 
 
SUBJECTIVE TYPE QUESTIONS
 
SHORT ANSWER TYPE QUESTIONS
 
1. Find the length of the tangent drawn to a circle of radius 8 cm, from a point which is at a distance of 10 cm from the centre of the circle.
 
2. A point P is 17 cm away from the centre of the circle and the length of tangent drawn from P to the circle is 15 cm. Find the radius of the circle.
 
3. There are two concentric circles, each with centre O and of radii 10 cm and 26 cm respectively. Find the length of the chord AB of the outer circle which touches the inner circle at P.
CBSE Class 10 Mathematics Circles Worksheet Set B 1
 
4. A and B are centres of circles of radii 9 cm and 2 cm such that AB = 17 cm and C is the centre of the circle of radius r cm which touches the above circles externally. If ÐACB = 90°, write an equation in r and solve it.
CBSE Class 10 Mathematics Circles Worksheet Set B 2
 
5. Two circles touch each other extemally at a point C and P is a point on the common tangent at C. If PA and PB are tangents to the two circles, prove that PA = PB.
CBSE Class 10 Mathematics Circles Worksheet Set B 3
 
6. Two circles touch each other internally. Prove that the tangents drawn to the two circles from any point on the common tangent are equal in length.
 
7. Two circles of radii 18 cm and 8 cm touch externally. Find the length of a direct common tangent to the two circles.
 
8. Two circles of radii 8 cm and 3 cm have their centres 13 cm apart. Find the length of a direct common tangent to the two circles .
 
9. Two circles of radii 8 cm and 3 cm have a direct common tangent of length 10 cm. Find the distance between their centres, upto two places of decimal.
 
10. With the vertices of DPQR as centres, three circles are described, each touching the other two extemally. If the sides of the triangle are 7 cm, 8 cm and 11 cm, find the radii of the three circles
 
LONG ANSWER TYPE QUESTIONS
 
1. DABC is a right-angled triangle with AB = 12 cm and AC = 13 cm. A circle with centre O has been inscribed inside the triangle. Calculate the value of x, the radius of the inscribed circle.
 
CBSE Class 10 Mathematics Circles Worksheet Set B 4
 
2. PQR is a right-angled triangle with PQ = 3 cm and QR = 4 cm. A circle which touches all the sides of the triangle is inscribed in the triangle. Calculate the radius of the circle.
 
 
3. In the given figure, O is the centre of each one of two concentric circles of radii 4 cm and 6 cm respectively. PA and PB are tangents to outer and inner circle respectively. If PA = 10 cm, find the length of PB, up to two places of decimal.
CBSE Class 10 Mathematics Circles Worksheet Set B 5
 
 
 
 
4. In the given figure, DABC is circumscribed. The circle touches the sides AB, BC and CA at P, Q, R respectively. If AP = 5 cm, BP = 7 cm, AC = 14 cm and BC = x cm, find the value of x.
 
CBSE Class 10 Mathematics Circles Worksheet Set B 6
 
5. In the given figure, quadrilateral ABCD is circumscribed. The circle touches the sides AB, BC, CD and DA at P, Q, R, S respectively. If AP = 9 cm, BP = 7 cm, CQ = 5 cm and DR = 6 cm, find the perimeter of quad. ABCD. 
CBSE Class 10 Mathematics Circles Worksheet Set B 7
 
 
6. In the given figure, the circle touches the sides AB, BC, CD and DA of a quadrilateral ABCD at the points P, Q, R, S respectively. If AB = 11 cm, BC = x cm, CR = 4 cm and AS = 6 cm, find the value of x.
CBSE Class 10 Mathematics Circles Worksheet Set B 7

 

 

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CBSE Class 10 Mathematics Chapter 10 Circles Worksheet

The above practice worksheet for Chapter 10 Circles has been designed as per the current syllabus for Class 10 Mathematics released by CBSE. Students studying in Class 10 can easily download in Pdf format and practice the questions and answers given in the above practice worksheet for Class 10 Mathematics on a daily basis. All the latest practice worksheets with solutions have been developed for Mathematics by referring to the most important and regularly asked topics that the students should learn and practice to get better scores in their examinations. Studiestoday is the best portal for Printable Worksheets for Class 10 Mathematics students to get all the latest study material free of cost.

Worksheet for Mathematics CBSE Class 10 Chapter 10 Circles

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Chapter 10 Circles worksheet Mathematics CBSE Class 10

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Chapter 10 Circles CBSE Class 10 Mathematics Worksheet

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