CBSE Class 10 Mathematics Circles Worksheet Set 02

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Review targeted practice sets for Class 10 Mathematics Chapter 10 Circles. Built according to official educational guidelines for the 2026-27 academic year, these downloadable worksheets support daily revision and core concept reinforcement.

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Access the complete worksheet PDF for Chapter 10 Circles below. Regular practice with these targeted questions builds familiarity with standard exam patterns and helps secure higher marks in final Mathematics evaluations.

Key Notes

  • Circles and its Related Terms : A Review
  • Angle Subtended by a Chord at a Point
  • Perpendicular from the Centre to a Chord
  • Circle through Three Points
  • Equal Chords and their Distances from the Centre
  • Angle Subtended by an Arc of a Circle
  • Cyclic Quadrilaterals

 

  • Circle- circle is locus of such points which are at equidistant from a fixed point in a plane.
  • Concentric circle- Circle having same centre called concentric circle.
  • Two arc of a circle called congruent if they have the same degree measure.
  • If two arc equal then their corresponding chords are equal.
  • The perpendicular from centre to chord of circle, it bisects the chord and converse.
  • There is one and only one circle passing through three non-collinear points.
  • Equal chords of circle are equidistant from centre.
  • The angle subtend by an arc at the centre of circle is twice the angle which subtend at remaining part of circumference.
  • Any two angles in the same segment of the circle are equal.
  • Angle of semicircle is right angle.
  • Equal chords of circle subtend equals angle at the centre of circle.
  • If the all vertices of a quadrilateral lie on the circumference of circle, then quadrilateral called cyclic.
  • In a cycle quadrilateral the sum of opposite angles is \( 180^\circ \) and converse.
  • The exterior angle of a cycle quadrilateral is equal to the opposite interior angle.

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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Download CBSE Practice Material: Class 10 Mathematics Chapter 10 Circles

Download Practice Sheet: Chapter 10 Circles (Class 10 Mathematics)

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Are these Mathematics Class 10 worksheets based on the 2026-27 competency-based pattern?

Yes, our CBSE Class 10 Mathematics Circles Worksheet Set 02 includes a variety of questions like Case-based studies, Assertion-Reasoning, and MCQs as per the 50% competency-based weightage in the latest curriculum for Class 10.

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