MathNet 2007-part-03 — 185 problems (EN–VI) Question 89

$ABCD$ is a cyclic quadrilateral in which $AB = 3$, $BC = 5$, $CD = 6$, and $AD = 10$. $M$, $I$, and $T$ are the feet of the perpendiculars from $D$ to lines $AB$, $AC$, and $BC$ respectively. Determine the value of $MI / IT$.