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## #1 2017-11-03 13:00:05

sydbernard
Member
Registered: 2017-09-04
Posts: 6

### Geometry help!

Construct a circle tangent to two given parallel lines and tangent from the outside to a disk lying between them.

I know that I need to construct a perpendicular between the 2 lines and bisect the segment which will then be the radius of the needed circle.  But I thought I had to add the radii from the two circles together then from the center of the given disk make the desired circle but it's not working out.

Last edited by sydbernard (2017-11-03 13:00:27)

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## #2 2017-11-03 23:14:24

alter ego
Member
Registered: 2012-03-30
Posts: 19

### Re: Geometry help!

Hi sydbernard,

I'm hoping I've understood this.  I'm slightly worried by the term disc rather than circle.

Let''s say the disc has radius r and the required circle has radius s.  The centre of the disc is O, and the line halfway between the parallels is m.

With centre O and radius r + s an arc cutting m at P will give the required circle centre.  So how to 'construct' r + s ?

If m cuts the disc at A, make a line perpendicular to m cutting one parallel at B.  AB = s. Extend OA and with centre A and radius AB make an arc to cut OA produced at C. Note: OC = r + s. With centre O and radius OC make an arc to cut m at P  P Is the required centre .

But what if the disc is too small to be cut by m ?

In that case you can draw a line n, perpendicular to m, through O. Let n cut the disc at E. Also draw any other line, FG, , parallel to n, so that F is on m and G on the parallel. FG = s.

Join F to E and construct GH parallel to FE with H on n. OE + EH = r + s so once again we have the right radius for an arc to cut m.

Alter

Last edited by alter ego (2017-11-03 23:25:31)

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