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Q.

Tangents drawn from the point  P(1,8) to the circle x2+y26x4y11=0   touch the circle at the points A and B then which of following statements are true 

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a

The  circum circle of ΔPAB  does not passes through centre of given circle

b

The  circum circle of  ΔPAB  must passes through centre of given circle 

c

Length of chord of contact of P w.r.t given circle is  4125  

d

Centre of circum circle of  ΔPAB is (2,5)

answer is B, C, D.

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Detailed Solution

circumcircle of ΔPAB  is
 (x1)(x3)+(y8)(y2)=0 x2+y24x10y+19=0
 
Length of chord of contact of P wrt given circle 
  =2rS11S11+r2=2241640=4125
 

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