A line cutting a circle at two points is a secant, and the tangent at any point is perpendicular to the radius, definitions that anchor this Class 10 circle sheet. The key also answers 12 cm for a chord length and 90° for the angle between a tangent and a radius.
Key Takeaways
A line meeting a circle at two points is a secant (Q1).
The tangent at any point is perpendicular to the radius (Q2).
The key records a chord length of 12 cm.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.A line that intersects a circle at two points is called a
(a) Tangent(b) Secant(c) Chord(d) Diameter
2.The tangent at any point of a circle is perpendicular to the
(a) Chord(b) Radius(c) Diameter(d) Secant
3.The length of the tangent drawn from an external point to a circle of radius 5 cm, where the distance of the point from the centre is 13 cm, is
(a) 12 cm(b) 8 cm(c) 18 cm(d) 5 cm
4.From an external point, the number of tangents that can be drawn to a circle is
(a) 1(b) 2(c) 3(d) Infinitely many
5.The angle between the tangent and the radius at the point of contact is
(a) 45°(b) 60°(c) 90°(d) 180°
6.Two tangents drawn from an external point to a circle are
(a) Unequal(b) Equal(c) Perpendicular(d) Parallel
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Define a tangent to a circle.
8.State the tangent-radius theorem.
9.A point is 13 cm away from the centre of a circle of radius 5 cm. Find the length of the tangent drawn from the point.
10.How many tangents can be drawn from a point inside a circle?
11.What is the angle between a tangent and the radius at the point of contact?
12.PA and PB are tangents drawn from an external point P to a circle. What is the relation between PA and PB?
13.How many tangents can be drawn to a circle from a point on the circle?
14.At how many points does a tangent touch a circle?
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.PA and PB are tangents from P to a circle with centre O. If ∠APB = 60°, find ∠AOB.
16.The length of the tangent from a point 10 cm away from the centre of a circle is 8 cm. Find the radius of the circle.
17.A tangent drawn from an external point to a circle is 12 cm long and the radius of the circle is 5 cm. Find the distance of the external point from the centre.
18.Two tangents PA and PB are drawn from a point P such that ∠APB = 90°. Find ∠AOB.
19.The radius of a circle is 6 cm. The distance of a point P from the centre is 10 cm. Find the length of the tangent drawn from P.
20.Prove that the tangents drawn from an external point to a circle are equal in length.
Answer Key
1. b) Secant
2. b) Radius
3. a) 12 cm
4. b) 2
5. c) 90°
6. b) Equal
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
What is a line that cuts a circle at two points called?
A secant, option (b) in this worksheet (Q1).
The tangent at any point of a circle is perpendicular to what?
The radius, option (b) in this worksheet (Q2).
What angle does a tangent make with the radius at the point of contact?
90°, from the answer key on this page.
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