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Ellehuny
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Dec0205, 08:29 PM (EST) 

"Geometry Construction HELP!"

I have to construct from two given circles, a common internal tangent. Problem is, I have no idea how to do this... its driving me crazy... geez I managed to finish most of the constructions due for my class but this one has me stumped. If you know how please advise (Step by step please)thanks! Ellen 

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alexb
Charter Member
1702 posts 
Dec0305, 03:23 AM (EST) 

3. "RE: Geometry Construction HELP!"
In response to message #2

>>>If you know how please advise (Step by step please) >> >>OK. Step #1: Can you draw a tangent from a point without a >>circle to the circle? > >I am not sure, i get where exactly are you going from here, This would be step #2. Let's wait a little. >but here's my attempt to make the first step a bit clearer  This step is in a different direction. Still, you come to the same point. 

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mpdlc
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Dec0405, 11:10 PM (EST) 

4. "RE: Geometry Construction HELP!"
In response to message #3

From the information posted, I understand that given two circumferences there are two pair of tangents one exterior and another one interior, and you are looking for a method to draw the interior one. I will give you below the procedure, I might be not the faster one but you will not forget easily, after over forty years I still able to recall it. The background of the method lays in the fact that the intersection points of the each pair of tangents are the two homothetic centers one direct and another one inverse of the two given circumferences. Firstly we will find these centers as follow. We call the bigger circumference W and the smaller w 1)Draw a line connecting the centers o1 and O1 of the given circumferences. 2)Draw two parallel radius R1 and r1 in each circumference. We call M1 and M2 the intersection points with W and analogously m1 and m2 for w. 3)Since we are focusing in the interior tangents only draw a line connecting M1 with m2. This line will intercept line O1o1 in a point we will call H2 which is the center of the inverse homothecy between the two circumferences. 4)Draw a circumference which has O1H2 as diameter (Obviously its center is the midpoint of O1H2). This circumference will cut circumference W in two points P1 and P2. 5)Now draw a line P1H2, this line is tangent also to circumference w. Do the same for P2 and the line P2H2 is the other interior tangent. If you were interested for the exterior tangents in step 3) you must connect M1 with m1 and follow analogous steps.


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