Two circles passing through `A(1,2), B(2,1)` touch the line `4x + 8y-7 = 0` at C and D such that ACED in a parallelogram. Then:
Text Solution
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The midpoint of AE must be the point of intersection of diagonals of parallelogram. Let `E -= (h,k)`. So, `((h+1)/(2),(k+2)/(2))` must lie on common tangent `4x+8y-7=0.` `:. 2h+4k+3=0` (1) Also, (h,k) lies on AB whose equation is `x+y=3`. `:. h+k=3` (2) Solving (1) and (2) , we get `h=(15)/(2),k= -(9)/(2)`
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