Constructing a Tangent to a Circle

Date: 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/