Chapter 16 Circles 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 ∠APB∠APB= 50°, find ∠AOB and ∠OAB.
Solution
2. In Fig. 16.121, it is given that O is the centre of the circle and ∠AOC = 150°. Find ∠ABC.
Solution
3. In Fig. 16.122, O is the centre of the circle. Find ∠BAC.
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)
(viii)
(x)
(xi)
(xii)
5. O is the circumcentre of the triangle ABC and OD is perpendicular on BC. Prove that ∠BOD = ∠A
6. In Fig. 16.135, O is the centre of the circle, BO is the bisector of ∠ABC. Show that AB = AC.
Solution
7. In Fig. 16.136, O is the centre of the circle, prove that ∠x = ∠y + ∠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 ∠ROS = 40°, find ∠RTS.
Solution
10. In Fig. 16.139, if ∠ACB = 40°, ∠DPB = 120°, find ∠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
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 ∠BOD = ∠A
Solution
6. In Fig. 16.135, O is the centre of the circle, BO is the bisector of ∠ABC. Show that AB = AC.
Solution
7. In Fig. 16.136, O is the centre of the circle, prove that ∠x = ∠y + ∠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.
9. In Fig. 16.138, O is the centre of a circle and PQ is a diameter. If ∠ROS = 40°, find ∠RTS.
10. In Fig. 16.139, if ∠ACB = 40°, ∠DPB = 120°, find ∠CBD.
Solution
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