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.

**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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