Let $\vartriangle ABC$ be a triangle. $I$ is the incentre of $\vartriangle ABC$, $BI$ and $AC$ meet at $D$, $CI$ and $AB$ meet at $E$. It is known that $DE = 12$ and $ADEI$ are concyclic. Suppose the circumradius of the $ADEI$ is $R$. Enter $R^2$.
Source:
Tags: geometry, circumcircle, incenter
Let $\vartriangle ABC$ be a triangle. $I$ is the incentre of $\vartriangle ABC$, $BI$ and $AC$ meet at $D$, $CI$ and $AB$ meet at $E$. It is known that $DE = 12$ and $ADEI$ are concyclic. Suppose the circumradius of the $ADEI$ is $R$. Enter $R^2$.