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Pentagon V1V2V3V4V5 made of vertices intersection of tangential pentagon T1T2T3T4T5 edges and its image U1U2U3U4U5 edges is cyclic with radius 4*s/((9 - h^2)sqrt(n)) where s is half perimeter, h = sqrt(1-2k), k = r/R and lambda = (1 - h^2)s^2n/(9 - h^2). Number n is root of a sextic equation h^6 n^6 - (h^2 + h - 3)(h^2 - h - 3)(h^2 - 3)h^2 n^5 - (7 h^4 - 41 h^2 + 63)h^2 n^4 - 18 (h^2 - 3) h^2 n^3 + (h^2 + 5 h + 3)(h^2 - 5 h + 3)n^2 + 5(h^2 - 3)n + 5 = 0

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