Bicentric Quadrilaterals

Mar 2020
1
0
Bulgaria
A bicentric quadrilateral $ABCD$ is inscribed in the circle $k_1(O_1;R)$ and circumscribes the circle $k_2(O_2;r)$. Let $V$ be the intersection point of the diagonals $AC$ and $BD$. Prove that $V, O_1$ and $O_2$ are collinear points.

A quadrilateral is bicentric if it's both inscriptable and circumscriptable. In other words, it is possible to draw a circle inside it which touches all four sides, and also to draw another circle around it, which passes through all four vertices. They have a number of interesting properties related to the two circles. This is one of them. Can you show me how to prove it?