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Two circles passing through A(1,2), B(2...

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: coordinates of E are

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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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