Class 10-Circles - Self Assessment 12 (EM)

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The concept of a Cyclic Quadrilateral and the specificity of its angles.

NOTE - 1 (The concept of a Cyclic Quadrilateral )

1) Which of the following is a cyclic quadrilateral? *

2 points

Fig - 1

Fig - 2

Fig - 3

NOTE-2(Specificity of the angles of a cyclic quadrilateral)

Video-The opposite angles of a Cyclic quadrilateral are supplementary (sum = 180) - [Watch this video carefully and answer the following questions]

2)In the picture,∠A= 70°, ∠B= 50°. Then find the following angles.( Hint : ABCD is a cyclic quadrilateral. Opposite angles of the cyclic quadrilateral are supplementary) *

2 points

100°

130°

110°

∠C ?

∠D ?

3) In the picture, ∠C= 85°, ∠D= 65° .Then find the following angles.( Hint : ABCD is a cyclic quadrilateral. Opposite angles of the cyclic quadrilateral are supplementary) *

4 points

115°

90°

95°

∠A ?

∠B ?

The angle on the alternate arcis half of the central angle of the arc.To remember this concept, watch the video below.

4)In the figure, O is the centre of the circle. ∠AOC= 100° , ∠BAO= 40° ,∠OAD= 30° .Then find the following angles.( Hint : ABCD is a cyclic quadrilateral. Opposite angles of the cyclic quadrilateral are supplementary .Also the angle on the alternate arc is half the central angle of the arc. *

6 points

130°

110°

50°

∠B ?

∠C ?

∠D ?

5) Find the following angles. *

6 points

120°

60°

100°

∠A ?

∠B ?

∠C ?

6) In the figure,AC is the diameter. Find the following angles.[Hint : Angle in a Semicircle is 90 °] *

9 points

50°

100°

90°

∠B ?

∠C ?

∠D ?

7)In the figure , AC and BD are diameters. Find the following angles.[Hint : Angle in a Semicircle is 90 °] *

9 points

45°

90°

50°

∠A ?

∠B ?

∠C ?

∠D ?

8)In the figure, AB is the diameter. Find the following angles.[Hint : Angle in a Semicircle is 90 °] *

6 points

70°

60°

140°

∠A ?

∠D ?

9)In the picture , AD is the diameter. Find the following angles. *

6 points

90°

40°

80°

∠DAB ?

∠ADC ?

SCHOOL *

10) Write this question in your notebook and send the answer to your Maths teacher. The teacher will tell you the marks of this question.

NAME *

DIVISION *

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