CBSE Class 10 Mathematics Circles Worksheet Set E

Read and download free pdf of CBSE Class 10 Mathematics Circles Worksheet Set E. 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

 

CIRCLES
 
Q.- A point P is 13 cm from the centre of the circle. The length of the tangent drawn from P to the circle is 12cm. Find the radius of the circle.
 
Sol. Since tangent to a circle is perpendicular to the radius through the point of contact.
Circles notes 9
∴ OTP = 90 0
In right triangle OTP, we have
OP2 = OT2 + PT2
=> 132 = OT2 + 122
=> OT2 = 132 – 122
= (13 – 12) (13 + 12) = 25
=> OT = 5
Hence, radius of the circle is 5 cm.
 
Q.-  Find the length of the tangent drawn from a point whose distance from the centre of a circle is 25 cm. Given that the radius of the circle is 7 cm.
 
Sol. Let P be the given point, O be the centre of the circle and PT be the length of tangent from P. Then, OP = 25 cm and OT = 7 cm.
Circles notes 10
Since tangent to a circle is always
perpendicular to the radius through the point of contact.
∴ OTP=90 0
In right triangle OTP, we have
OP2 = OT2 + PT2
=> 252 = 72 + PT2
=> PT2 = 252 – 72
= (25 – 7) (25 + 7)
= 576
=> PT = 24 cm
Hence, length of tangent from P = 24 cm

 

 
SECTION A: 
 
1. A line touches a circle of radius 4 cm. Another line is drawn which is tangent to the circle. If the two lines are parallel then find the distance between them. (8 cm)
 
2. From a point P, which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR are drawn to the circle. Find the area of the quadrilateral PQOR. (60 cm2)
 
3. In the fig. 1, QR is a common tangent to given circle which meet at T. Tangent at T meets QR at P. If QP = 3.8 cm, then find the length of QR. (7.6 cm)
 
CBSE Class 10 Mathematics Circles Worksheet Set E 1
 
SECTION B: 
 
4. If d1, d2 (d2>d1) be diameters of two concentric circles, c be the length of a chord of the circle which is tangent to the other circle, prove that d22 = c2 + d12.
 
5. In fig. 2, if CP = 11 cm and BC = 7 cm, then find the length of BR.
 
6. In fig. 3, find the value of x. (4 cm) (60⁰)
CBSE Class 10 Mathematics Circles Worksheet Set E 2
 
 
SECTION C: 
 
7. In fig. 4, if angle between two tangents drawn from a point P to a circle of radius a and centre O is 60°, then prove that AP = a √3 .
 
8. In the given fig. 5, AB and AC are two tangents to a circle from an external point A. DE is a line segment touching the circle at F and intersecting AB at D and AC at E. Prove that AB = 1/2 (perimeter of ΔADE )
 
9. In fig. 6, ABC is a right triangle in which ∠B ∠ 90 0 . A circle is inscribed in the triangle. If AB = 8 cm and BC = 6 cm, find the radius r of the circle.
CBSE Class 10 Mathematics Circles Worksheet Set E 3
 
SECTION D: 
 
10. In fig.7, a tangent PT and a line segment PBA is drawn to a circle with centre O. If OL ⊥ AB, prove that PA x PB = PT2.
 
11. In fig.8, QR is tangent at Q. PR‖AQ, where AQ is a chord through A and P is a centre, the end point of the diameter AB. Prove that BR is tangent at B.
 
12. Let s denote the semi- perimeter of a triangle ABC in which BC = a, CA = b and AB = c. If a circle touches the sides BC, CA, AB at D, E and F respectively, prove that BD = (s-b).

CBSE Class 10 Mathematics Circles Worksheet Set E 4

 

 

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Chapter 10 Circles CBSE Class 10 Mathematics 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. Teachers of studiestoday have referred to the NCERT book for Class 10 Mathematics to develop the Mathematics Class 10 worksheet. After solving the questions given in the practice sheet which have been developed as per the latest course books also refer to the NCERT solutions for Class 10 Mathematics designed by our teachers. After solving these you should also refer to Class 10 Mathematics MCQ Test for the same chapter. We have also provided a lot of other Worksheets for Class 10 Mathematics which you can use to further make yourself better in Mathematics.

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