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C1 and C3 share two intersection points, A and C. The linear line l passing through the two points obeys the linear equation
l: 2rkx+ 2r(1+¡î(1-k^2 ))y-〖2r〗^2 (1+¡î(1-k^2 ))=0 ....... (6)
Therefore, the vertical distance d2 from the point O to line l can be calculated as follows;
d2 = |-〖2r〗^2 (1+¡î(1-k^2 ))|/¡î(4r^2 k^2+4r^2 (1+2¡î(1-k^2 )+1-k^2)) = (〖2r〗^2 (1+¡î(1-k^2 )))/¡î(8r^2 (1+¡î(1-k^2 ))) = (〖2r〗^2 (1+¡î(1-k^2 ))¡î(8r^2 (1+¡î(1-k^2 ))))/(8r^2 (1+¡î(1-k^2 ))) =(2r¡î(2+2¡î(1-k^2 )) )/4 =
(¡î(1+k)+¡î(1-k))/2 r ...................... (7)
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IEEE/ICACT20210142 Slide.13
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