# 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 $$(a, b, r)$$.

×