Question 12
Suppose 4 sides $AB$, $BC$, $CD$, $DA$ of a quadrilateral $ABCD$ are tangent to a circle with its center $O$, and conditions
$$
OA = 5,\ OB = 6,\ OC = 7,\ OD = 8
$$
are satisfied. Let $M$, $N$ be the midpoint of the line segments $AC$, $BD$ respectively. Find the value of $OM : ON$. Here for a line segment $XY$ its length is also denoted by $XY$.
$$
OA = 5,\ OB = 6,\ OC = 7,\ OD = 8
$$
are satisfied. Let $M$, $N$ be the midpoint of the line segments $AC$, $BD$ respectively. Find the value of $OM : ON$. Here for a line segment $XY$ its length is also denoted by $XY$.