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

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

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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