Two Lengths

  1. A, B and C are in a straight line. AB=BD=CD=1. AD=AC. Find BC.
  2. 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.
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