Geometry Questions?

Question

There are 3 questions I need help with.. I'm not sure how to do them.. Work for the problem is good so then I can try to figure them out also!

http://i185.photobucket.com/albums/x8/hamsandwhich326/3.jpg question 1

http://i185.photobucket.com/albums/x8/hamsandwhich326/2.jpg question 2

http://i185.photobucket.com/albums/x8/hamsandwhich326/1.jpg question 3

Answer 1

(1) Make a right triangle with OB = 30 (since it is the same length as radius given as 30). Then use Pythagorean Theorem a^2 + b^2 = c^2, or 24^2 + x^2 = 30^2, to find half of length AB. Then double that to find full length AB.
900 - 576 = 324 = x^2
so x = 18 and AB = 36

(2) Again use a^2 + b^2 = c^2 to find
9^2 + r^2 = (r+4)^2 and solve for r.
81 + r^2 = r^2 + 8r + 16
65 = 8r
r = 8.1

(3) Similar triangles means sides are proportional.
So set up ratios as equivalent fractions:
x / 12 = 8.4 / 14
x / 12 = 84 / 140 (multiply by 10 to get rid of decimal)
x / 12 = 3 / 5 (reduce fraction)
then cross multiply
(x)(5) = (12)(3)
x = 36 / 5 = 7.2

Note: Plug in your answers back into the problems and check your work.