Given a random point $A$ outside the circle, and a circle centered at $C$, how do I construct a line that is tangent to the circle $C$ passing through $A$, using only Euclid's elementary constructions?
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It is impossible if the point is inside the circle. Otherwise it is trivial if the center of the circle is known. – user Mar 01 '18 at 20:38
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No, I wasn't so clear. The point is outside the circle. – John Glenn Mar 01 '18 at 20:40
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You can do that also without knowing the point $C$. You can even to that without a compass, with a straight egde alone. :) – CiaPan Mar 01 '18 at 21:10
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How do you propose to do that? – John Glenn Mar 01 '18 at 21:11
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1@JohnGlenn Please see a description at A tangent to a circle with a straight edge. – CiaPan Mar 03 '18 at 12:02
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Very clever! @CiaPan – John Glenn Mar 03 '18 at 12:07
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I have just found a similar question at Construct tangent to a circle, asked in October '12. – CiaPan Mar 04 '18 at 19:10
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Draw a circle with diameter $CA$. Its intersection with the original circle will give the tangent points.
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