Geometry Problem 1541 Challenge: Unveiling BG Length in an Inscribed Quadrilateral with Harmonic Quaternary Insight for Academic Pursuits

In a circle with center O and diameter AB, the inscribed quadrilateral ABCD has diagonals that intersect at E. The circumcircle of triangle BCE intersects OB at F. Given that AF is 16 and FB is 6, find the length of BG.

Geometry Problem 1541 Challenge: Unveiling BG Length in an Inscribed Quadrilateral with Harmonic Quaternary Insight for Academic Pursuits

Problem 1541
Geometry's test,
Harmonic Quaternary guide,
BG length concealed.
Challenge embraced, insight unveiled,
Quadrilateral's secret revealed.

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