Circle of Midpoints of Secants

Geometry Level 4

Consider the circle \( x^2 + y^2 = 25 \), and a point \( A (1, 2) \) lying inside it. Next consider secants of the circle passing through point \(A\). It turns out that the midpoints of the secants, lie on another circle of center \( (a, b) \) and radius \( r \).

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


Inspiration.

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