Today our topic of discussion is Mathematics Circle Exercises 8.5.
Mathematics Circle Exercises 8.5
Exercise 8.5
- The angle inscribed in a major arc is-
1) acute angle
2) obtuse angle
4) complementary angle
3) right angle
- What is the value of the angle z in the circle with centre O?
1) 126°
2) 108 °
3) 72 °
4) 54 °
- In the adjacent figure 1/2∠ECD = how much degrees?
1) 40°
2)50°
3) 80°
4) 100°
- 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
- 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
- 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
- What is the value of ∠BOC?
1) 300 °
2) 270°
3) 120 °
4) 90 °
- 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
- Draw a tangent to a circle which is parallel to a given straight line.
- Draw a tangent to a circle which is perpendicular to a given straight line
- Draw two tangents to a circle such that the angle between them is 60 °
- 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.
- Draw an ex-circle to an equilateral triangle ABC touching the side AC of the triangle, the length of each side being 5 cm.
- Draw the inscribed and the circumscribed circles of a square.
- If the chords AB and intersect at an internal point E, prove that, ∠AEC = 1/2(∠BOD+∠AOC)
- 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.
- 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.
- 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.
- 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.
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