Two Lengths

A, B and C are in a straight line.
AB=BD=CD=1.
AD=AC.
Find BC.

Perpendicular lines CA and CB are both tangent to circle O with
radius 4.
AB passes through O, the center of the circle.
AO intersects the circle at D.
BO intersects the circle at E.
If BE=1, find AD.
Source: rec.puzzles, Eva Zerz in July 1995,
Dennis Yelle in February, 1996.
Solution
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