Mathematics Circle Exercises 8.5

Today our topic of discussion is Mathematics Circle Exercises 8.5.

Mathematics Circle Exercises 8.5

 

 

Exercise 8.5

1. The angle inscribed in a major arc is-

1) acute angle

2) obtuse angle

4) complementary angle

3) right angle

2. What is the value of the angle z in the circle with centre O?

1) 126°

2) 108 °

3) 72 °

4) 54 °

3. In the adjacent figure 1/2∠ECD = how much degrees?

1) 40°

2)50°

3) 80°

4) 100°

4. Two circles intersects each other externally. If one of their diametes is 8 c m and the radius of the another is 4 c m, what is the distance between their two centres?

1) 0

2) 4

3) 8

4) 12

5. If two tangents PQ and PR are drawn from the external point P in a circle

with centre O, then triangle PQR will be-

(i) isosceles

(ii) equilateral

(iii) right angled

Which one the following is correct?

1) i

2) i and ii

3) ii and iii

4) i, ii and iii

6. If O is the circumcentre of the equilateral triangle ABC, then ∠BOC = how much degrees?

1) 30 °

2) 60 °

3) 90 °

4) 120 °

8) AB and AC are the tangents of the circle BCD. Centre of the circle in O and ∠BAC = 60 °. According to this information answer the questions 

7. What is the value of ∠BOC?

1) 300 °

2) 270°

3) 120 °

4) 90 °

8. If D be the midpoint of the arc BDC ,then

(i) ∠BDC = ∠BAC

(ii) ∠BAC = 2 ∠BOC

(ii) ∠BOC = ∠DBC+ ∠BCD

Which one of the following is correct?

1) i and ii

2) i and iii

3) ii and iii

4) i, ii and iii

 

 

9. Draw a tangent to a circle which is parallel to a given straight line.
10. Draw a tangent to a circle which is perpendicular to a given straight line
11. Draw two tangents to a circle such that the angle between them is 60 °
12. Draw the circumcircle of the triangle whose sides are 3cm 4 c.m. and 4.5 c.m. and find the radius of this circle.
13. Draw an ex-circle to an equilateral triangle ABC touching the side AC of the triangle, the length of each side being 5 cm.
14. Draw the inscribed and the circumscribed circles of a square.
15. If the chords AB and intersect at an internal point E, prove that, ∠AEC = 1/2(∠BOD+∠AOC)
16. AB is the common chord of two circles of equal radius. If a line segment drawn from the point B meet through the circles at P and Q, prove that, ΔPAQ is an isosceles triangle.
17. The chord AB = x cm and ODL AB, are in the circle ABC with centre O. use the adjoint figure to answer the following questions:

1) Find the area of the circle.

2) Show that, D is the mid point of AB.

3) If OD = (-2) cm, determine the value of x.

18. In the figure, YM and ZM are internal bisectors of ∠Y and ∠Z respectively and YN and ZN are external bisectors of ZY ZZ.

1) Show that,∠ MYZ+∠NYZ = 90°

2) Prove that, ∠YNZ=90°- 1

3) Prove that, Y, M, Z and N are concyclic.

 

 

19. The lengths of three sides of a triangle are 4 cm, 5 cm and 6 cm. Use this information to answer the following questions:

1) Construct the triangle.

2) Draw the circumcircle of the triangle.

3) From an exterior point of the circumcircle, draw two tangents to it and show that their lengths are equal.