Note since T r is the sum of independent and identically distributed random variables as r gets larger the distribution approaches a Normal distribution by the Central Limit Theorem. The Gamma Distribution is also defined for non-integer values of r by a different formula. We won't cover that. Pick a point at random on a unit disc. Top and bottom loop each only last the minimum time of their respective components.
Entire loop lasts as long as maximum of the two loops.
Just apply the ideas on maximum and minimum like in Example 4, page 317.