VTMO 2026 - Grade 9 - Semifinal - SET 2 - Self-study Question 8

Two circles with centres O,I and radii 4,10 respectively intersect at A,B. The internal bisector of $\angle OAI$ meets the circles again at C,D respectively. Given $OI=2\sqrt{39}$, and J is the circumcenter of triangle BCD, find $OJ^2$.