CBSE Class 10 Mathematics Circles Worksheet Set A

Read and download free pdf of CBSE Class 10 Mathematics Circles Worksheet Set A. 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.- From a point P, 10 cm away from the centre of a circle, a tangent PT of length 8 cm is drawn. Find the radius of the circle.
 
Sol. Let O be the centre of the given circle and let P be a point such that
Circles notes 1
OP = 10 cm.
Let PT be the tangent such that PT = 8 cm.
Join OT.
Now, PT is a tangent at T and OT is the
radius through T.
∴ OT ⊥ PT.
In the right ΔOTP, we have
OP2 = OT2 + PT2 [by Pythagoras’ theorem]
=> OT = √OP2 - PT2 =√ (10)2 - (8)2 cm
= √36 cm = 6 cm.
 
Q.- Prove that in two concentric circles, the chord of the larger circle which touches the smaller circle, is bisected at the point of contact.
 
Sol. Given : Two circles with the same centre O and AB is a chord of the larger circle which touches the smaller circle at P.
Circles notes 2
To prove : AP = BP.
Construction : Join OP.
Proof : AB is a tangent to the smaller circle
at the point P and OP is the radius through P.
∴ OP ⊥ AB.
But, the perpendicular drawn from the centre of a circle to a chord bisects the chord.
∴  OP bisects AB. Hence, AP = BP.

 

 
VERY SHORT ANSWER TYPE QUESTIONS
 
1. In the given figure, TAS is a tangent to the circle, with centre O, at the point A. If ÐOBA = 32°, find the value of x.
CBSE Class 10 Mathematics Circles Worksheet Set A 1
 
2. In the given figure, ABC is a right angled triangle right angled at A, with AB = 6cm and AC = 8 cm. A circle with centre O has been inscribed inside the triangle. Calculate the value of r, the radius of the inscribed circle.
CBSE Class 10 Mathematics Circles Worksheet Set A 2

3. In the given figure, PT is tangent to the circle at T. If PA = 4 cm and AB = 5 cm, find PT.

CBSE Class 10 Mathematics Circles Worksheet Set A 3

 

4. In the figure, O is the centre of the circle, PQ is tangent to the circle at A. If ÐPAB = 58°, find ÐABQ and ÐAQB.
CBSE Class 10 Mathematics Circles Worksheet Set A 4
 
5. In figure, a circle touches the side BC of DABC at P and touches AB and AC produced at Q and R respectively. If AQ = 5 cm, find the perimeter of DABC.
CBSE Class 10 Mathematics Circles Worksheet Set A 5
6. A tangent PT is drawn parallel to a chord AB as shown in figure. Prove that APB is an isosceles triangle.
CBSE Class 10 Mathematics Circles Worksheet Set A 6
 
7. In figure, XP and XQ are two tangents to a circle with centre O from a point X outside the circle. ARB is tangent to circle at R. Prove that XA + AR = XB + BR.

CBSE Class 10 Mathematics Circles Worksheet Set A 7

 
 
8. In fig, if ÐATO = 40°, find ÐAOB.
CBSE Class 10 Mathematics Circles Worksheet Set A 8

 

9. In fig., CP and CQ are tangents to a circle with centre O. ARB is another tangent touching the circle at R. If CP = 11 cm and BC = 7 cm, then find the length of BR. 
CBSE Class 10 Mathematics Circles Worksheet Set A 9
 
10. In fig., DABC is circumscribing a circle. Find the length of BC.
CBSE Class 10 Mathematics Circles Worksheet Set A 10
 
 

 

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CBSE Class 10 Mathematics Chapter 10 Circles Worksheet

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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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Worksheet for CBSE Mathematics Class 10 Chapter 10 Circles

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