**Q1. If the chord of 6 cm in length of a circle makes an angle of 45° with tangent drawn at it’s vertex then what will be the radius of that circle ?**

(a) 6√2 cm

(b) 5 cm

(c) 3√2 cm

(d) 6 cm

**Q2. The radius of a circle is 13 cm and the distance of its chord XY from centre is 12 cm. Then length of that chord is **

(a) 15 cm

(b) 12 cm

(c) 10 cm

(d) 20 cm

**Q3. Suppose in ∆ABD , ∠ADB = 20° and C is a point on BD such as AB = AC and CD = CA. Then what will be the measure of ∠ABC ?**

(a) 40°

(b) 45°

(c) 60°

(d) 30°

**Q4. If G is the centroid and AD is a median of a triangle ABC, if AD is 12 cm then AG is?**

(a) 10 cm

(b) 6 cm

(c) 4 cm

(d) 8 cm

**Q5. ∆ABC is a right angled triangle. AD is a perpendicular to hypotenuse BC. If AC = 2 AB, then value of BD is equal to ?**

(a) BC/4

(b) BC/5

(c) BC/2

(d) BC/3

**Q6. In a right angled triangle ABC, AB = 2.5 cm, cos B = 0.5, ∠ACB = 90°. Length of side AC in cm is equals to ?**

(a) 5⁄4√3

(b) 5⁄16√3

(c) 5√3

(d) 5⁄2√3

**Q7. Two circles of radii 4 cm and 9 cm respectively touch externally at a point and a common tangent touches them at points P and Q respectively. Then what will be the area of the square with side PQ ?**

(a) 97 cm square

(b) 194 cm square

(c) 72 cm square

(d) 144 cm square

**Q8. Two tangents are drawn from point P to a circle at points A and B. O is the centre of circle. Then if ∠AOP = 60°, then ∠APB = ?**

(a) 120°

(b) 90°

(c) 60°

(d) 30°

**Q9. AB is the diameter of a circle with centre O. CD is a chord which is equal to radius in length. AC and BD are produced to meet at P. Then ∠APB will be of **

(a) 30°

(b) 60°

(c) 90°

(d) 120°

**Q10. If G be the centroid of ∆ABC and if AG = BC then what will be the measure of ∠BGC ?**

(a) 45°

(b) 90°

(c) 63°

(d) 75°

**Q12. Two circles each of radii r cut each other and passes through others centre. Then length of common chord is**

(b) √3 r

(c) √3/2 r

(d) √5 r

**Q13. Tangents drawn at two points P and Q lying on circumference of a circle cut each other at A , if ∠PAQ = 68°, then ∠APQ is ?**

(a) 56°

(b) 68°

(c) 28°

(d) 34°

**Q14. In ∆ABC internal angle bisector of ∠C cuts AB at point D. In this AB ≠ AC and E is a point on CD such that AE = AD. If ∠ABC = 50° then ∠CAE is equal to ?**

(a) 40°

(b) 50°

(c) 30°

(d) 25°