Two circles having equal radii #r_1# and touching a line #l#on the same side of #l# are at a distance of #x# from each other. Third circle of radius #r_2# touches the two circles. How do we find the height of third circle from #l#?

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Answer 1 · 2017-07-06T11:46:06

See below.

Supposing that #x# is the distance between perimeters and

supposing that #2(r_1+r_2)gt x+2r_1# we have

#h = sqrt((r_1+r_2)^2-(r_1+x/2)^2)+r_1-r_2#

#h# is the distance between #l# and the perimeter of #C_2#