Geometry Problem 1151: Circle, Diameter, Chord, Perpendicular, 90 Degrees, Metric Relations. Level: School, College, Mathematics Education

The figure below shows a circle O of diameter AB perpendicular to a chord CD at E. A chord AF intersects CD at G. If EH is perpendicular to AF, prove that CE² = AG.HF 
 

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Isolines of Problem 1151