Circle GeometryDate: 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/ |
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