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Step-by-step NCERT solutions for Circles (Chapter 10, CBSE Class 10 Mathematics) — the full working for every question, not just the final answer. You can also read the Circles textbook chapter.

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What these solutions cover

All 17 questions in Circles are solved in the PDF. Here's what's inside, exercise by exercise:

Tangent to a Circle — Introduction

  1. How many tangents can a circle have?
  2. Fill in the blanks:
    • (i) A tangent to a circle intersects it in ___ point(s).
    • (ii) A line intersecting a circle in two points is called a ___.
    • (iii) A circle can have ___ parallel tangents at the most.
    • (iv) The common point of a tangent to a circle and the circle is called ___.
  3. A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is: (A) 12 cm (B) 13 cm (C) 8.5 cm (D) √119 cm
  4. Draw a circle and two lines parallel to a given line such that one is a tangent and the other, a secant to the circle.

Properties of Tangents

  1. From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is: (A) 7 cm (B) 12 cm (C) 15 cm (D) 24.5 cm
  2. In the given figure, if TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then ∠PTQ is equal to: (A) 60° (B) 70° (C) 80° (D) 90°
  3. If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80°, then ∠POA is equal to: (A) 50° (B) 60° (C) 70° (D) 80°
  4. Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
  5. Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.
  6. The length of a tangent from a point A at distance 5√2 cm from the centre of the circle is 5 cm. Find the radius of the circle.
  7. Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
  8. A quadrilateral ABCD is drawn to circumscribe a circle (see figure). Prove that AB + CD = AD + BC.
  9. In the given figure, XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X'Y' at B. Prove that ∠AOB = 90°.
  10. Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.
  11. Prove that the parallelogram circumscribing a circle is a rhombus.
  12. A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively. Find the sides AB and AC.
  13. Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
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More solutions in Mathematics

01Real Numbers02Polynomials03Pair of Linear Equations in Two Variables04Quadratic Equations05Arithmetic Progressions06Triangles07Coordinate Geometry08Introduction to Trigonometry09Some Applications of Trigonometry11Areas Related to Circles12Surface Areas and Volumes13Statistics14Probability
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More NCERT Solutions for Class 10

Read the Circles textbook chapter / PDF, or browse all CBSE Class 10 Mathematics solutions.

← PreviousCh 9: Some Applications of TrigonometryNext →Ch 11: Areas Related to Circles

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