Class Exercise 5 – 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. 9

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In the above figure, a circle is having center at W and radius 8. A square LMNO is circumscribed about the circle, then LN =?
                A.   12√3
                B.    10√2
                C.   16√2
                D.    4√π
                E.    18

Solution;

As LMNO is a square and circumscribed the circle. LO will be tangent to circle, if we draw a line from center of circle as WP, it will make a right angled triangle LPW.

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WP = Radius of circle = 8
As LMNO is square so each side of it will be = Diameter of circle
Hence, LP = radius of circle = 8
Using Pythagorean Theorem we can easily find  the side ‘LW’ of the triangle LPW.
LW 2 = LP2   +  PW2
                = 82  +  82
                = 64 + 64
                = 128
Taking square root both side,
LW =   8√2
LW = WN = 8√2
So,          LN = LW + WN
                                = 8√2 + 8√2
                                = 16√2

So correct answer choice is ‘C’.

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Q.10        Triangle ACB is inscribed in a circle. AB is equal to diameter of circle

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                                   Quantity A                                                   Quantity B
                                         Angle ‘A’                                                  Angle ‘C’
          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;

As per review of circle, when any triangle is inscribed in a circle and one of the sides of the triangle is diameter of circle then that will be right angled triangle.
So, angle C = 90°, and angle A and angle B in any case have to be lesser than angle C.
Hence quantity B i.e Angle C will  be greater than quantity A.

 The correct answer choice is ‘B’.

                                                               

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