Find the area of the minor segment of a circle of radius 14 cm,

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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 
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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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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.

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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 ]




Radius of the circle, r = 14 cm

The chord AB subtends an angle 60o at the centre of the circle.
Now,

Area space of space circle space equals space πr squared space equals space 22 over 7 space straight x space left parenthesis 14 right parenthesis squared space equals space 616 space cm squared

Area space of space sector space AOB space equals space πr squared space straight x space 60 over 360 space space

equals space 616 space space straight x space 1 over 6 space equals space 308 over 3 space equals space 102.67 space cm squared space left parenthesis approx right parenthesis

In space increment OAB comma
space
AO space equals space OB space left parenthesis space radii space of space the space circle right parenthesis

therefore space angle OBA space equals space angle OAB space
left parenthesis space in space straight a space triangle comma space equal space sides space have space equal space angels space opposite space to space them right parenthesis

Now comma
angle space OAB space plus space angle OBA space plus space angle AOB space equals space 180 degree space left square bracket Angle space sum space property right square bracket

rightwards double arrow space 2 angle space OAB space plus space 60 to the power of straight o space equals space 180 to the power of straight o

rightwards double arrow space 2 angle space OAB space equals space 180 degree space minus 60 degree space equals space 120 degree

rightwards double arrow space angle OAB space equals space 60 degree

Thus comma space increment AOB space thin space is space an space equilateral space triangle.

therefore space Area space of space increment AOB space equals space fraction numerator square root of 3 over denominator 4 end fraction left parenthesis OA right parenthesis squared
space equals space fraction numerator square root of 3 over denominator 4 end fraction space straight x space left parenthesis 14 right parenthesis squared space equals space fraction numerator 196 square root of 3 over denominator 4 end fraction space equals space 84.87 space cm squared

Area of the minor segment = Area of the sector AOB - Area of ΔAOB

= 102.67 - 84.87
= 17.85 cm2

Now, 
Area of the major segment = Area of the circle  - Area of the minor segment

=616 - 17.8

= 598.2 cm2
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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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