Given a cyclic quadrilateral ABCD and let A_{1}, B_{1}, C_{1}, D_{1} the incenters and
r_{a}, r_{b}, r_{c}, r_{d} the inradii of the triangles BAD, ABC, BCD, ADC. Then (1)
A_{1}B_{1}C_{1},D_{1} is a rectangle, (2) r_{a } + r_{c } = r_{b } +
r_{d}

This sangaku problem was proposed by Maruyama Ryoukan in 1800. References: Fukagawa Hidetoshi, Tony Rothman, "Sacred Mathematics: Japanese Temple Geometry" (Princenton University Press, 2008).

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