An Arc by Construction

Geometry Level pending

Consider the circle \( x^2 + y^2 = 49 \), and a point \( A (6, 8) \) lying outside it. Lines are drawn through point \(A\) such that they intersect the circle, and form secants. It turns out that the midpoints of the secants, lie on a circular arc with center \( (a, b) \) and radius \( r \).

Find the triplet \( (a, b, r) \).


Inspiration.

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