Practice Questions: Circles | Mathematics (Maths) Class 10 PDF Download

Questions

1. Given a right triangle PQR which is right-angled at Q. QR = 12 cm, PQ = 5 cm. The radius of the circle which is inscribed in triangle PQR will be?

2. How many tangents can be drawn from the external point to a circle?

3. From an external point P, tangents PA and PB are drawn to a circle with centre O. If ∠PAB = 50°, then find ∠AOB.

4. In given figure, PQ is a tangent at a point C to a circle with centre O. If AB is a diameter and ∠CAB = 30°, find ∠PCA.

5. In given figure, a circle is inscribed in a ΔABC, such that it touches the sides AB, BC and CA at points D, E and F respectively. If the lengths of sides AB, BC and CA are 12 cm, 8 cm and 10 cm respectively, find the lengths of AD, BE and CF.

6. From a point P which is at a distance of 13 cm from the centre O of the circle of radius 5 cm, the pair of the tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is

(a) 60 cm² 
(b) 65 cm²
(c) 30 cm² 
(d) 32.5 cm²

7. True/False
When the chord AB makes an angle of 60° at the circle’s centre, the angle between the tangents on A and B is at 60°.

8. The length of the tangent for the external point on the circle is always greater than the circle’s radius.

9.  Fill in the blanks:
(i) A tangent to the circle cuts it in _______________ point(s).

(ii) A line intersecting the circle in two points is called a ___________________.

(iii) A circle could have _____________________ parallel tangents at the most.

(iv) The common point of the tangent to the circle and the circle is called ________________________.

10. A tangent PQ at the point P of the circle of radius 5 cm meets the line passing through the centre O at the point Q such that OQ = 12 cm. What will be the length of PQ?

11.  If tangents PA and PB from a point P to a circle with centre O are inclined to each other at an angle of 80°, then ∠ POA is equal to?

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

13. Two tangents are drawn to a circle from an external point P, touching the circle at the points A and B and a third tangent intersects segment PA in C and segment PB in D and touches the circle at Q. If PA = 20 units, then find the perimeter of ∆PCD.

14. In fig., PQ and PR are tangents drawn from P. If ∠QPR = 40°, then find ∠QSR.

15. In the given figure, PA and PB are tangents to the circle from an external point P. CD is another tangent touching the circle at Q. If PA = 12 cm, QC = QD = 3 cm, then find PC + PD.

Answers

1. The radius of the circle will be 2 cm.

2. Two tangents can be drawn from the external point to a circle.

3. ∠AOB = 100º

4. ∠PCA = 60º

5. AD = 7 cm, BE = 5 cm and CF = 3 cm.

7. False.

8. False.

9. (i) A tangent to the circle cuts it into one point(s).

(ii) A line intersecting the circle in two points is called a secant.

(iii) A circle could have two parallel tangents at the most.

(iv) The common point of the tangent to the circle and the circle is called the point of contact.

10. PQ = √119 cm

11. ∠POA is 50°.

12. The length of the chord of the larger circle is 8 cm.

13. The perimeter of ∆PCD is 40 units.

14. ∠QSR = 70° 

15. PC + PD = 18cm