1. Given a right triangle PQR which is rightangled 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 cm^{2}
(b) 65 cm^{2}
(c) 30 cm^{2}
(d) 32.5 cm^{2}
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.
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.
6. (a) 60 cm27. 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
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1. What are some popular hobbies that involve circles? 
2. How can I incorporate circles into my creative hobbies? 
3. What are the benefits of engaging in hobbies that involve circular movements? 
4. Are there any specific tools or equipment needed for circlerelated hobbies? 
5. How can I find local groups or classes for circlebased hobbies? 

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