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Q.

Consider the circle x2+y2=25 and a point A(1,2) lying inside it. Consider secants of the circle passing through the point A. It turns out that the midpoint of the secants, lie on another circle of centre (a,b) and radius r, then the value of  a+b+2r2=________
 

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answer is 4.

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Detailed Solution

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Let Px1,y1 be the midpoint of the chord 
Equation of the chord is S1=S11
xx1+yy125=x12+y1225x12+y12x1xy1y=0A(1,2)x12+y12x12y1=0x2+y2x2y=0C12,1,r=52a+b+2r2=12+1+52=4.
 

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