MathDB

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

Source:

January 4, 2021

geometryCyclictangentialsquare

Problem Statement

ABCD

is a quadrilateral having both an inscribed circle (one tangent to all four sides) with center

I,

and a circumscribed circle with center

O

. Let

S

be the point of intersection of the diagonals of

ABCD

. Show that if any two of

S, I

and

O

coincide, then

ABCD

is a square (and hence all three coincide).