Class Exercise 4 – Circle

Circles Review – Fundamentals of CirclesFormulas for Circle,  Congruent CirclesTangent to a circlePolygon inscribed in a Circle  , Circle inscribed in a circleConcentric Circles

Class Questions –  Exercise 1         Exercise 2      Exercise 3        Exercise 4      Exercise 5

Practice QuestionsSolutions

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Q.7                     In the following figure, the radius of the circle with center at “O” is 12 then what is the area of shaded region?   Find the value.

cir-19

Solution;

                First find out the area of circle = π r2
                                                                                = π x 122
                                                                                = 144π
                Next ,  we will calculate the area of triangle LOM,
                                                                                                = 1/2  x 12 x 12
                                                                                                = 72
                Area occupied by the quarter portion of circle = area of circle/4
                                                                                                             = 144 π/ 4
                                                                                                              =      36π                                                                                                                                                                                                                                                                                                         = 36 x 3.14
                                                                                                                = 113.04
                Hence area of shaded region = 113.04 – 72
                                                                                = 41.04

                                                                                              

Q.8
The below figure shows two concentric circles with center P.  The area of outer circle is double the area of inner circle.

cir-20

                           Quantity A                                           Quantity B
                        Area of Inner circle                      Area of shaded region
     A.  If Quantity A is greater
     B.  If Quantity B is greater
     C.  If Quantity A and Quantity B are equal
     D.  The relationship cannot be determined from given information

Solution;

If we take radius of inner circle = r, then
Area of inner circle = π x r2
Area of Outer circle = double the inner circle
                              = 2 x π x r2
Area of shaded region = Area of Outer circle – Area of Inner Circle
                                   = 2 x π x r2  –  π x r2
                                    =  π x r2 = πr2
Hence the area of inner circle will be equal to area of shaded region .

The correct answer choice is C.

                                                                                                      

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