Centroid to Circumcenter

Geometry Level pending

Let A B C ABC be an acute-angled triangle such that A C B = 4 5 \angle{ACB} = 45^{\circ} . Let G G be the point of intersection of the three medians and let O O be the circumcentre. Suppose O G = 1 OG=1 and O G B C OG \parallel BC . Determine the length of the segment B C BC .


The answer is 12.

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