QUESTIONS Chapter 9 Pages XXXXXXXXXX 32) 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...

QUESTIONS
Chapter 9 Pages 318-320
32) 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.
Chapter 10 pages 359-361.
6) Find the length of the chord that cuts off arc of length in a circle of diameter 33.
16) Prove Proposition 32 of the Maasei Hoshev:


20) One of the problems from the Maasei Hoshev: 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?
Chapter 11 Pages 379.
8) 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 .
Reference
Katz, Victor.
A History of Mathematics An Introduction. Pearson Education, Inc., 2009. Print
QUESTIONS
Chapter 9 Pages 318-320
32) 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.
Chapter 10 pages 359-361.
6) Find the length of the chord that cuts off arc of length in a circle of diameter 33.
16) Prove Proposition 32 of the Maasei Hoshev:


20) One of the problems from the Maasei Hoshev: 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?
Chapter 11 Pages 379.
8) 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 .
Reference
Katz, Victor.
A History of Mathematics An Introduction. Pearson Education, Inc., 2009. Print