#### Chapter 16 CirclesÂ R.D. Sharma Solutions for Class 9th Exercise 16.4

**Exercise 16.4**

1. In Fig. 16.120, O is the centre of the circle. If âˆ APBâˆ APB= 50Â°, find âˆ AOB and âˆ OAB.

2. In Fig. 16.121, it is given that O is the centre of the circle and âˆ AOC = 150Â°. Find âˆ ABC.

3. In Fig. 16.122, O is the centre of the circle. Find âˆ BAC.

4. If O is the centre of the circle, find the value of x in each of the following figures.

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(x)

(xi)

(xii)

5. O is the circumcentre of the triangle ABC and OD is perpendicular on BC. Prove that âˆ BOD = âˆ A

6. In Fig. 16.135, O is the centre of the circle, BO is the bisector of âˆ ABC. Show that AB = AC.

7. In Fig. 16.136, O is the centre of the circle, prove that âˆ x = âˆ y + âˆ z.

8. In Fig. 16.137, O and O' are centres of two circles intersecting at B and C. ACD is a straight line, find x.

9. In Fig. 16.138, O is the centre of a circle and PQ is a diameter. If âˆ ROS = 40Â°, find âˆ RTS.

10. In Fig. 16.139, if âˆ ACB = 40Â°, âˆ DPB = 120Â°, find âˆ CBD.

11. A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc.

**Solution****Solution****Solution**4. If O is the centre of the circle, find the value of x in each of the following figures.

**Solution**(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(ix)

(x)

(xii)

5. O is the circumcentre of the triangle ABC and OD is perpendicular on BC. Prove that âˆ BOD = âˆ A

**SolutionÂ**

6. In Fig. 16.135, O is the centre of the circle, BO is the bisector of âˆ ABC. Show that AB = AC.

**Solution**7. In Fig. 16.136, O is the centre of the circle, prove that âˆ x = âˆ y + âˆ z.

**Solution**8. In Fig. 16.137, O and O' are centres of two circles intersecting at B and C. ACD is a straight line, find x.

**Solution**9. In Fig. 16.138, O is the centre of a circle and PQ is a diameter. If âˆ ROS = 40Â°, find âˆ RTS.

**Solution**10. In Fig. 16.139, if âˆ ACB = 40Â°, âˆ DPB = 120Â°, find âˆ CBD.

**SolutionÂ**

11. A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc.

**Solution**