Example 2:  Line AB is tangent to circle O, and angle ACB is a right angle.   Find the lengths of  AC and BC. 

Solution:  Angle CAB measures half of 120^o, or 60^o.  Therefore triangle ACB is a 30-60-90 triangle, so AC is half the hypotenuse, or 6 units, and BC is AC times the square root of 3:

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