In the given figure, a triangle ABC is drawn to circumscribe of

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 Multiple Choice QuestionsMultiple Choice Questions

161. The area of quadrant of a circle whose circumference is 22 cm is
  • 7 over 2 space cm squared
  • 7 cm2

  • 3 cm2

  • 3 cm2

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162. If the perimeter and the area of a circle are numerically equal, then the radius of the circle is
  • 2 units  
  • 11 units
  • 4 units 
  • 4 units 
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163. A chord of circle of radius 10 cm subtends a right angle at the centre. The area of minor segment APBA is (Fig. 12.92).


  • 28 cm2  
  • 28.2 cm2
  • 28.5 cm2  
  • 28.5 cm2  
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 Multiple Choice QuestionsShort Answer Type

164.

In Fig.  find the area of the shaded region, enclosed between two concentric circles of radii 7 cm and 14 cm where ∠AOC = 40°. (use π =22/7)

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165.

In the given figure, a triangle ABC is drawn to circumscribe of radius 3 cm, such that the segments RD and DC are respectively of length 6 cm and 9 cm. If the area of ΔABC is 54 cm2, then find lengths of sides AB and AC.


Suppose the given circle touch the sides AB and AC of the triangle at point F and E, respectively. Let the length of the line segment AF is x cm.


We know that the length of tangents drawn from an external point to a circle are equal.

In ΔABC,

CE = CD = 9 cm (Tangents of the circle from point C)

BF = BD = 6 cm (Tangents on the circle from point B)

AE = AF + FB = x + 6

BC = BD + DC = 6 + 9 = 15

CA = CE + EA  = 9 + x

Area space of space increment OBC space equals space 1 half space straight x space BC space straight x space OD space
space equals space 1 half space straight x space 15 space straight x space 3 space equals space 45 over 2

Area space of space increment OCA space equals space 1 half space straight x space AC space straight x space OE space
equals 1 half space straight x space left parenthesis straight x plus 9 right parenthesis space straight x space 3 space equals space 3 over 2 left parenthesis straight x space plus space 9 right parenthesis

Area space of space increment OAB space equals space 1 half space straight x space AB space straight x space OF
equals 1 half space straight x space left parenthesis space straight x space plus space 6 right parenthesis space straight x space 3 space space equals space 3 over 2 space left parenthesis space straight x space plus space 6 right parenthesis

Area space of space increment ABC space equals space Area space of space increment OBC space plus increment OCA space plus Area space of space increment OAB
space 54 space equals space 45 over 2 space plus 3 over 2 space left parenthesis straight x space plus space 9 right parenthesis space plus 3 over 2 space left parenthesis space straight x space plus space 6 right parenthesis

rightwards double arrow space 54 space equals space 45 space plus space 3 straight x space

rightwards double arrow space 3 space straight x space equals space 54 space minus space 45

rightwards double arrow space straight x space equals space 3

Therefore comma

AB space equals space straight x plus space 6 space equals space 3 space plus space 6 space equals space 9 space cm

and space AC space equals space 9 space plus space straight x space equals space 9 space plus space 3 space equals space 12 space cm

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166.

Find the area of the minor segment of a circle of radius 14 cm, when its central angle is 60°. Also find the area of the corresponding major segment.  [ use π = 22/7 ]

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 Multiple Choice QuestionsLong Answer Type

167. Prove that the tangent drawn at the midpoint of an arc of a circle is parallel to the chord joining the end points of the arc.
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168.

In Fig., AB and CD are two diameters of a circle with centre O, which are perpendicular to each other. OB is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.   Use π = 227

               


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169.

In Figure 2, ABCD is a trapezium of area 24.5 sq. cm. In it, AD|| BC,  DAB = 90°, AD = 10 cm and BC = 4 cm. If ABE is a quadrant of a circle, find the area of the shaded region.    Take π= 227                  

                     


 Multiple Choice QuestionsShort Answer Type

170.

In Figure, two concentric circles with centre 0, have radii 21 cm and 42 cm. If ∠ AOB = 60°, find the area of the shaded region.  Use π = 227

                         

 


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