Associated Topics || Dr. Math Home || Search Dr. Math

### Distance between Points of Tangency

```Date: 02/16/2003 at 19:20:37
From: Glavy
Subject: Geometry

Two circles, one of radius 5, the other of radius 8, intersect at
exactly one point, and the center of each circle lies outside the
other circle. A line is externally tangent to both circles. Find the
distance between the two points of tangency.

Thank you!
```

```
Date: 02/17/2003 at 03:49:18
From: Doctor Floor
Subject: Re: Geometry

Hi, Glavy,

Let C1 and C2 be the centers of the two circles, where C1 belongs to
the circle with radius 5. Let T1 and T2 be the points of tangency of
these circles with the common externally tangent line.

We know that C1T1 = 5 and C2T2 = 8 and that both are perpendicular to
the common tangent T1T2. We also know that C1C2 = 5+8 = 13.

Now we have the following sketch:

T1------ ? --------T2
|                 |
5|                 |5
|                 |
|                 |
|                 |
C1-----------------X
`-._            |
`-._       |3
13   `-._  |
C2

In this sketch C1X is parallel to T1T2 and thus perpendicular to
T2C2. Now we can find C1X and thus T1T2 by Pythagoras' Theorem.

If you have more questions, just write back.

Best regards,
- Doctor Floor, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
College Euclidean Geometry
High School Euclidean/Plane Geometry

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search