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### 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,

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/
```
Associated Topics:
High School Conic Sections/Circles
High School Constructions
High School Geometry

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