Circles

What you'll learn

A clear guide to tangents to a circle — the point of contact, the two key theorems, and the tangent-length formula — with a real-life analogy, a worked Pythagoras example and a self-check quiz.

This chapter has

Circles — solved practice questions

8 Class 10 Mathematics questions with step-by-step solutions. Attempt each, then reveal the answer.

1. Q1easy

   A tangent to a circle touches the circle at:

   • Atwo points
   • Bexactly one point
   • Cthree points
   • Dno point
   Show answer & solution

   Correct answer: (B) exactly one point

   A tangent touches the circle at exactly one point, called the point of tangency.

2. Q2easy

   The tangent to a circle at any point is _____ to the radius at that point.

   • Aperpendicular
   • Bparallel
   • Cequal
   • Dbisecting
   Show answer & solution

   Correct answer: (A) perpendicular

   The tangent is always perpendicular to the radius drawn to the point of tangency.

3. Q3easy

   How many tangents can be drawn from an external point to a circle?

   • A1
   • B2
   • C3
   • Dinfinite
   Show answer & solution

   Correct answer: (B) 2

   Exactly 2 tangents can be drawn from any external point to a circle.

4. Q4medium

   If PA and PB are tangents from external point P to a circle, then:

   • APA = PB
   • BPA > PB
   • CPA < PB
   • DPA + PB = diameter
   Show answer & solution

   Correct answer: (A) PA = PB

   Tangent segments from an external point are equal → PA = PB.

5. Q5hard

   If PA and PB are two tangents from P with ∠APB = 80°, then ∠AOB (O = centre) is:

   • A80°
   • B90°
   • C100°
   • D120°
   Show answer & solution

   Correct answer: (C) 100°

   ∠APB + ∠AOB = 180° (since OA ⊥ PA and OB ⊥ PB in quadrilateral OAPB). ∠AOB = 100°.

6. Q6medium

   A tangent drawn from an external point P touches the circle (radius 5 cm) at T. If PT = 12 cm, then OP (O = centre) is:

   • A5 cm
   • B12 cm
   • C13 cm
   • D17 cm
   Show answer & solution

   Correct answer: (C) 13 cm

   OT ⊥ PT → OP² = OT² + PT² = 25 + 144 = 169 → OP = 13 cm.

7. Q7easy

   The number of tangents that can be drawn to a circle from a point ON the circle is:

   • A0
   • B1
   • C2
   • Dinfinite
   Show answer & solution

   Correct answer: (B) 1

   From a point on the circle exactly one tangent can be drawn.

8. Q8hard

   Two concentric circles have radii 5 cm and 3 cm. The length of the chord of the outer circle that is tangent to the inner circle is:

   • A4 cm
   • B6 cm
   • C8 cm
   • D10 cm
   Show answer & solution

   Correct answer: (C) 8 cm

   The chord is tangent to inner circle → distance from centre to chord = 3 cm. Half-length = √(5²−3²) = 4 → chord = 8 cm.

Want the full set? Practise all 15 Circles questions →