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
]]>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.
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