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1)

 The radius of the circle  passing through the points (5,7),(2,-2) and (-2,0) is


A) 2 units

B) 5 units

C) 3 units

D) 4 units

Answer:

Option B

Explanation:

 Given, points  (5,7) ,(2,-2) and (-2,0) lie on circle

 Let (h,k) be centre of circle 

    OA=OC

162021904_m3.JPG

   (h+2)2+k2=(h5)2+(k7)2

h2+4h+4+k2=h210h+25+k214k+49

14h+14k=70

     h+k=5    .............(i)

 When OA=OB

    (h+2)2+k2=(h2)2+(k+2)2

 h2+4h+4+k2=h24h+4+k2+4k+4

8h4k=4

 2h-k=1       .........(ii)

 From eqs. (i) and (ii)  we get

 h=2, k=3

  Centre of circle (2,3)

 Radius of circle OA=  (2+2)2+32

  OA=  42+32=16+9=25=5units