MathDB

6

Part of 2013 NZMOC Camp Selection Problems

Problems(1)

criterion for bicentric ABCD to be a square (2013 NZOMC Camp Sel. p6)

Source:

1/4/2021
ABCDABCD is a quadrilateral having both an inscribed circle (one tangent to all four sides) with center I,I, and a circumscribed circle with center OO. Let SS be the point of intersection of the diagonals of ABCDABCD. Show that if any two of S,IS, I and OO coincide, then ABCDABCD is a square (and hence all three coincide).
geometryCyclictangentialsquare