CBSE Class 10 Mathematics Circles Worksheet Set A

Question. A chord of a circle of radius 10 cm subtends a right angle at its centre. The length of the chord (in cm) is
(a) 5√2
 (b) 10√2
(c) 5/√2
(d) 10√3

Answer: D

Question. In the given figure, PA and PB are tangents to the circle with centre O. If ∠APB = 60°, then ∠OAB is
(a) 30°
(b) 60°
(c) 90°
(d) 15°

Answer: A

Question. The length of the tangent drawn from a point 8 cm away from the centre of circle of radius 6 cm is
(a) 7 cm
(b) 2 7 cm
(c) 10 cm
(d) 5 cm

Answer: B

Question. From a point Q, the length of the tangent to a circle is 12 cm and the distance of Q from the centre is 15 cm. The radius of the circle is
(a) 9 cm
(b) 12 cm
(c) 15 cm
(d) 24.5 cm

Answer: A

Question. Two concentric circles of radii 13 cm and 5 cm are given. The length of the chord of the larger circle which touches the smaller circle is
(a) 16 cm
(b) 4 cm
(c) 24 cm
(d) 10 cm

Answer: C

Question. Two concentric circles of radii a and b where a > b, are given, the length of a chord of the larger circle which touches the other circle is
(a) a² − b²
(b) 2√a² − b²
(c) a² + b²
(d) 2√a² + b²

Answer: B

Question. At one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn to the circle.
The length of the chord CD parallel to XY and at a distance 8 cm from A is
(a) 4 cm
(b) 5 cm
(c) 6 cm
(d) 8 cm

Answer: D

Question. A tangent to a circle is a line that touches the circle at exactly
(a) two points
(b) three points
(c) one point
(d) none of the options

Answer: C

Question. If the angle between two radii of a circle is 140°, then the angle between the tangents at the ends of the radii is
(a) 90°
(b) 50°
(c) 70°
(d) 40°

Answer: D

Question. The radii of two concentric circles are 16 cm and 10 cm. AB is a diameter of the bigger circle. BD is tangent to the smaller circle touching it at D. Find the length of AD.
(a) 3√130 cm
(b) 2√139 cm
(c) 2√130 cm
(d) 4√139 cm

Answer: B

Question. If two tangents inclined at an angle 60° are drawn to a circle of radius 3 cm, then length of each tangent is equal to
(a) (3/2)√3 cm
(b) 6 cm
(c) 3 cm
(d) 3√3 cm

Answer: D

Question. How many tangents can a circle have from a point lying inside the circle ?
(a) 2
(b) infinitely many
(c) 1
(d) none of these

Answer: D

Question. Two parallel lines touch the circle at points A and B. If area of the circle is 16p cm², then AB is equal to
(a) 5 cm
(b) 8 cm
(c) 10 cm
(d) 16 cm

Answer: B

Question. If four sides of a quadrilateral ABCD are tangent to a circle, then
(a) AC + AD = BD + CD
(b) AB + CD = BC + AD
(c) AB + CD = AC + BC
(d) AC + AD = BC + DB

Answer: B

3. In the given figure, PT is tangent to the circle at T. If PA = 4 cm and AB = 5 cm, find PT.

6. A tangent PT is drawn parallel to a chord AB as shown in figure. Prove that APB is an isosceles triangle.

 

7. In figure, XP and XQ are two tangents to a circle with centre O from a point X outside the circle. ARB is tangent to circle at R. Prove that XA + AR = XB + BR.

 

 

8. In fig, if ÐATO = 40°, find ÐAOB.

Please click on below link to download CBSE Class 10 Mathematics Circles Worksheet Set A