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

×