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Circle Geometry

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Date: 6/4/96 at 17:29:36
From: Anonymous
Subject: Circle Geometry

Two circles intersect at A and N. One of their common tangents has
points of contact P and T. Prove that <PAT and <PNT are supplementary.

I know that 'supplementary' means that the angles have to add up to
180 degrees.

I don't know what to do becuase there are 2 circles, so you can't use
other theorems like 'Tangent Cord Theorem' or 'Tangent Theorem'.

Thank you very much.

Sheryl Korenzvit
```

```
Date: 6/5/96 at 17:3:3
From: Doctor Ceeks
Subject: Re: Circle Geometry

You want <PAT + <PNT = 180, which is equivalent to showing
<PAT+<P'AT '= 180 where P' and T' are the points of contact of the
other common tangent.  But this is equivalent to showing
<PAP' + < TAT'=180.  Now notice that the radii through P and T are
parallel since both are perpendicular to PT.  Also the radii through
P' and T' are parallel since both are perpendicular to P'T'.  We
conclude that the arc PP' not through A and the arc TT' not through A
together measure 360, and the problem follows.

Please write back if you need more explanation.

Doctor Ceeks,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Conic Sections/Circles
High School Geometry

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