Circumcenters and Orthocenters (ID: 7)
Problem status: not solved
The circumradius of acute triangle \(ABC\) is \(1\). Let \(O\) be the circumcenter of \(ABC\) and \(H\) be the orthocenter of \(ABC\). Also, let \(A'\) be the circumcenter of triangle \(BHC\) and \(OA' = \frac{8}{5}\). The length of \(BC\) can be written in form \(\frac{a}{b},\) where \(a\) and \(b\) are positive relatively prime integers. Find \(a+b\).
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