Question 1:
Show directly without the use of Ptolemy's theorem, that in an isosceles trapezoid, the square on a diagonal is equal to the sum of the product of the two parallel sides plus the square on one of the other sides.
1 Find the length of the chord that cuts off arc of length 5 1/2 in a circle of diameter 33.
2) Prove Proposition 32 of the Maasei Hoshev:
3) One of the problems from the MaaseiHoshev: A barrel has various holes: The first hole empties the full barrel in 3 days; the second hole empties the full barrel in 5 days; another hole empties the full barrel in 20 hours; and another hole empties the full barrel in 12 hours. All the holes are opened together. How much time will it take to empty the barrel?
Question 2:
It turns out that in the Balinese calendar, to specify a day, it is sufficient to specify the position of the day in just the five, six, and seven day weeks. Thus, we specify a day by the notation 
Find the minimum number of days between the day 
.