To construct:
First, construct circle c1 with center O and an arbitrary point Q not on the circle. Next, construct a line through O and Q. Construct a segment OQ and it's midpoint N. Then, construct circle c2 using N as its center and ON as its radius. Construct the points of intersection, P and R, between the circles c1 and c2. Finally, construct segments PQ and QR, which are tangent lines to circle c1 through point Q (labeled as t1 and t2 on the following sketch).
Mathematical facts:
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Here is the script (for those that like to play).
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