Question

The radius of circle O is 28, and OC =9. What is the length of AB?

Answer 1

The answer:
the complement of the question proposed one of the choices given beneath:
a) 58.8
b) 53.0
c) 29.4
d) 26.5

as we observe at the figure, AOB an isosceles triangle, and OCB is a right triangle

consider OCB
OC =9, OB= radius = 28
the problem is how to find the length of CA, for that C is a midpoint of segment AB, so AC=BC

BC can be found by using pythagorean theorem
OB²= OC² + CB²,  this implies CB² = OB² - OC²

CB² = 28² - 9² = 784 - 81=703, therefore CB= sqrt (703)=26.51

CB=26.51, since CB= AC, so  AC=CB= 26.51

finally the the length of AB is AB = 2 x CB = 2x AC= 2x 26.51= 53.0

the answer is b) 53.0