# Circle and chord

Geometry Level 5

If the values of $$a$$ for which the common chord of circles $$x^2+y^2=8$$ and $$(x-a)^2+y^2=8$$ subtends right angle at the origin are $$a_{1},a_{2},\ldots ,a_{n},$$ then find $$n+\displaystyle \sum^{n}_{j=1}a_{j}+\displaystyle \prod^{n}_{j=1}a_{j}$$.

×