**Q1. The length of the chord of a circle is 8 cm and perpendicular distance between centre and the chord is 3 cm. Then the radius of the circle is equal to:**

(a) 4 cm

(b)5 cm

(c)6 cm

(d)8 cm

**Q2. P and Q are the middle points of two chords (not diameters) AB and AC respectively of circle with centre at a point O. The lines OP and OQ are produced to meet the circle respectively at the points R and S. T is any point on the major arc between the point R and S of the circle. If ∠BAC = 32°, ∠RTS =?**

(a) 32°

(b) 74°

(c) 106°

(d) 64°

**Q3. If O be the circumcentre of a triangle PQR and ∠QOR = 110°, ∠OPR = 25°, then the measure of ∠PRQ is-**

(a) 65°

(b) 50°

(c) 55°

(d) 60°

**Q4. A, B, C, D are four points on a circle. AC and BD intersect at a point E such that ∠BEC = 130° and ∠ECD = 20°, ∠BAC is –**

(a) 120°

(b) 90°

(c) 100°

(d) 110°

**Q5. Two circles touch each other internally. Their radii are 2 cm and 3 cm. The biggest chord of the greater circle which is outside the inner circle is of length –**

**Q6. AB is the chord of a circle with centre O and DOC is a line segment originating from a point D on the circle and intersecting AB produced at C such that BC = OD. If ∠BCD = 20°, then ∠AOD is equal to-**

(a) 20°

(b) 30°

(c) 40°

(d) 60°

**Q7. In a circle of radius 17 cm, two parallel chords of lengths 30 cm and 16 cm are drawn. If both the chords are one the same side of the centre, then the distance between the chords is-**

(a) 9 cm

(b) 7 cm

(c) 23 cm

(d) 11 cm

**Q8. If the arcs of square length in two circles subtend angles of 60° and 75° at their centres, the ratio of their radii is-**

(a) 3: 4

(b) 5:4

(c) 5: 5

(d) 3: 5

**Q9. If two concentric circles are of radii 5 cm and 3 cm, then the length of the chord of the larger circle which touches the smaller circle is –**

(a) 6 cm

(b) 7 cm

(c) 10 cm

(d) 8 cm

**Q10. O is the in centre of the ∆ABC, if ∠BOC = 116°, then ∠BAC is –**

(a) 42°

(b) 62°

(c) 58°

(d) 52°

**Q11. A, B and C are three points on a circle such that the angles subtended by the chords AB and AC at the centre O are 90° and 110° respectively. Further suppose that the centre ‘O’ lies in the interior of ∠BAC. Then ∠BAC is –**

(a) 20°

(b) 40°

(c) 80°

(d) 160°

**Q14. The area of a circle is 324𝜋 sq.cm. The length of its longest chord (in cm.) is-**

(a) 28

(b) 32

(c) 36

(d) 38

**Q15. AB is a diameter of a circle with centre O. The tangents at C meets AB produced at Q. If ∠CAB = 34°, then measure of ∠CBA is-**

(a) 34°

(b) 124°

(c) 56°

(d) 68°