Geometry Problem 1540: Solving for the Length of Chord in a Circle: Analyzing Intersections and Given Values for Academic Pursuits

Consider a circle with center O and diameter AB. We draw the chord AC. The circle with diameter OC intersects AC at point G and OA at point D. From point A, a line is drawn that intersects CD at point E and the arc BC at point F. Given that AE = 3 and EF = 13, we need to determine the length of AC.

$Geometry Problem 1540: Solving for the Length of Chord in a Circle: Analyzing Intersections and Given Values for Academic Pursuits$

Problem 1540
Intersecting lines,
Circle's secret in their grasp,
Given clues align.
Chord's length, a mystery unveiled,
Geometry's dance unfolds.

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