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## mckenzieandjesus one year ago is tangent to circle O at B. What is the length of the radius r? Round to the nearest tenth. 15.4 6.1 1.7 2.9

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1. mckenzieandjesus

2. mckenzieandjesus

@jim_thompson5910

3. mckenzieandjesus

@Hero

4. Hero

@mckenzieandjesus, What kind of triangle is ABO?

5. mckenzieandjesus

acute?

6. mckenzieandjesus

wait a right?

7. Hero

If segment AB is tangent to circle O at point B, what does that say about segments AB and OB? Yes, it is a right triangle. Which means what?

8. mckenzieandjesus

its 90 degrees

9. mckenzieandjesus

AB and OB are equal?

10. Hero

Well, you're given two sides of the right triangle and need to find the length of the third side. What rule do we use for this situation?

11. mckenzieandjesus

Pythagorean theorem?

12. mckenzieandjesus

a2 + b2 = c2?

13. Hero

Exactly. $$a^2 + b^2 = c^2$$

14. mckenzieandjesus

$10 ^{2}+11.7 ^{2} = 236 \frac{ 89 }{ 100 }$

15. mckenzieandjesus

236 89/100^2 = 56116.8721

16. Hero

Actually, you have to find the correct "a", "b" and "c" when using the pythagorean theorem.

17. mckenzieandjesus

how do i do that?

18. Hero

"a" and "b" are always the "legs" of the right triangle. "c" is always the hypotenuse. Sometimes, they give you "a" and "c", but not "b".

19. mckenzieandjesus

10+1.7= 11 7/10

20. mckenzieandjesus

can u help with this one? Point P is the center of two concentric circles. PQ = 10.5 and PS = 20.9. RS is tangent to the smaller circle and a chord of the larger circle. What is length of RS to the nearest tenth? 36.1 41.4 31.4 41.8

21. Hero

Your work for the problem you originally posted is not correct.

22. mckenzieandjesus

this one?

23. Hero

ya, this one.

24. mckenzieandjesus

i did it wrong? how?

25. mckenzieandjesus

10^2+1.7^2= 102 89/100?

26. mckenzieandjesus

@Hero

27. Hero

I thought you already learned about right triangles. I'm going to say it again. Sometimes, you're given "c" instead of "b", which means, if you have something like a = 3 c = 5 then you have to solve for b: a^2 + b^2 = c^2 3^2 + b^2 = 5^2 b^2 = 5^2 - 3^2 b^2 = 25 - 9 b^2 = 16 b = 4

28. mckenzieandjesus

i got 132.89 how do i make it smaller?

29. mckenzieandjesus

11.5?

30. mckenzieandjesus

10^2+11.5^2= 232 1/4

31. mckenzieandjesus

232.25

32. mckenzieandjesus

still lost.. @Hero

33. mckenzieandjesus

@pooja195

34. Hero

Yes, I can tell. I think I know something that might be useful for you. Try ixl.com

35. mckenzieandjesus

ok..

36. mckenzieandjesus

@jim_thompson5910

37. mckenzieandjesus

i did it in the steps u showed me @Hero

38. Hero

In this case, a = r b = 10 c = 11.7 So $$a^2 + b^2 = c^2$$ becomes: $$r^2 + 10^2 = 11.7^2$$ You subtract 10^2 from both sides: $$r^2 = 11.7^2 - 10^2$$ Then square root both sides to get $$r = \sqrt{11.7^2 - 10^2}$$

39. Hero

You'll have to finish simplifying $$r$$ on your own. I'm not going to do that for you. Just let me know what you get. I'll say whether or not it's right or wrong.

40. mckenzieandjesus

square root 11.7^2-10^2 = 6.073713856?

41. mckenzieandjesus

6.1?

42. Hero

Correct.

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