Constructing a Tangent to a CircleDate: 03/19/99 at 13:21:55 From: Tahira lopez Subject: Constructions Construct a tangent to a circle through a given point not on the circle. Date: 03/20/99 at 06:47:39 From: Doctor Floor Subject: Re: Constructions Hi Tahira, Thanks for your question! Let C be the midpoint of the circle, and P the point outside the circle, through which point we are given the task of constructing a tangent to the circle. Suppose that Q will be the point where this tangent will meet the circle. Then angle(PQC) will be 90 degrees, so Q must be on the circle with diameter PC. This gives the following construction: * Construct the midpoint M of PC. You can find how to do this in our archives: http://mathforum.org/dr.math/problems/zaidi11.13.98.html * Draw the circle with center M passing through C. * Let Q and Q' be the two intersections of the two circles. * PQ and PQ' are the two possible tangents we were looking for. Here is a picture: If you have a math question again, please send it to Dr. Math. Best regards, - Doctor Floor, The Math Forum http://mathforum.org/dr.math/ |
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