CLASS 10 · CHAPTER 10

Circles
Practice Questions

20 curated NCERT & Board Exam questions to test your understanding. Click on "Show Solution & Answer" to check step-by-step working.

20Questions

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Q1MCQ1 Mark

Tangent PT at point P of circle of radius 5 cm meets line through centre O at point T so OT = 12 cm. Length PT is:

Q2MCQ1 Mark

From point Q, length of tangent to circle is 24 cm and distance of Q from centre is 25 cm. Radius is:

Q3MCQ1 Mark

If TP and TQ are two tangents to circle with centre O so that ∠POQ = 110°, then ∠PTQ is:

Q4MCQ1 Mark

If tangents PA and PB from point P to circle with centre O are inclined to each other at angle 80°, then ∠POA is:

Q5Assertion-Reason1 Mark

Assertion (A): The tangent at any point of a circle is perpendicular to the radius through the point of contact. Reason (R): Length of tangents drawn from an external point to a circle are equal.

Q6Assertion-Reason1 Mark

Assertion (A): A circle can have infinitely many tangents. Reason (R): A tangent intersects a circle at exactly one point.

Q7Short Answer2 Marks

Prove that tangents drawn at the ends of a diameter of a circle are parallel.

Q8Short Answer2 Marks

Prove that perpendicular at point of contact to tangent to circle passes through centre.

Q9Short Answer2 Marks

Two concentric circles are of radii 5 cm and 3 cm. Find length of chord of larger circle which touches smaller circle.

Q10Short Answer2 Marks

A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.

Q11Short Answer2 Marks

Prove that parallelogram circumscribing a circle is a rhombus.

Q12Long Answer3 Marks

Prove that lengths of tangents drawn from an external point to a circle are equal.

Q13Long Answer3 Marks

Triangle ABC is drawn to circumscribe circle of radius 4cm such that segments BD and DC are 8cm and 6cm. Find sides AB and AC.

Q14Long Answer3 Marks

Prove that angle between two tangents from external point is supplementary to angle subtended by segment joining points of contact.

Q15Long Answer3 Marks

Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at center.

Q16Case Study4 Marks

Case Study Scenario: A round clock has tangents drawn from point P outside. PA = 12 cm and P is 13 cm from center O. Question: Find radius of clock and area of quadrilateral OAPB.

Q17Case Study4 Marks

Case Study Scenario: A circular park is circumscribed by quadrilateral ABCD. Question: If AB = 6 cm, BC = 7 cm, CD = 4 cm, find AD.

Q18PYQ5 Marks

In figure, XY & X'Y' are parallel tangents. Tangent AB with point of contact C intersects XY at A & X'Y' at B. Prove ∠AOB = 90°.

Q19PYQ5 Marks

PQ is chord of length 8 cm of circle of radius 5 cm. Tangents at P and Q intersect at T. Find length TP.

Q20PYQ5 Marks

Circles Practice Questions