## OpenSessame 2 years ago In circle O, CD = 44, OM = 20, ON = 19, CD is perpendicular to OM and EF to ON. a. Find the radius. If your answer is not an integer, express it in radical form. b. Find FN. If your answer is not an integer, express it in radical form. c. Find EF. Express it as a decimal rounded to the nearest tenth.

1. OpenSessame

2. mathstudent55

You mean CD is perpendicular to OM and EF to ON, right?

3. OpenSessame

Yea dont know why i wrote parallel

4. mathstudent55

Can you find MD?

5. OpenSessame

No...

6. mathstudent55

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7. OpenSessame

Its a right triangle? so can you you the Pythagorean theorem?

8. mathstudent55

In the circle above, radius OP is perpendicular to chord AC.

9. mathstudent55

Radius OP bisects chord AC, so AB = BC

10. mathstudent55

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11. mathstudent55

Now look at your figure again. Notice segment OM and chord CD. What is the length of MD?

12. OpenSessame

22?

13. mathstudent55

Right. Now draw the radius OD. Since you know two sides of a right triangle, you can find the third side.

14. OpenSessame

$\sqrt{884}$

15. mathstudent55

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16. mathstudent55

Correct, but you can simplify it.

17. OpenSessame

Should I because it says just leave it in radical form...

18. OpenSessame

I can simplify it myself i know how to do that part lol, but i just need help with the rest!

19. mathstudent55

Ok. Next. What is FN?

20. OpenSessame

Would that be 22? Because they are perpendicular?

21. mathstudent55

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22. OpenSessame

Oh wait no! i get it! dont tell me!!

23. mathstudent55

Notice that ON is not the same length as OM, so that side has different dimensions except for the radius which is obviously the same anywhere in the circle.

24. OpenSessame

$\sqrt{523}$

25. mathstudent55

Correct. Great job!

26. OpenSessame

Now EF?

27. mathstudent55

Now EF is easy.

28. OpenSessame

Its just double right?

29. mathstudent55

Right, but the write it as a decimal rounded off to the nearest tenth.

30. OpenSessame

Okay, I got it! Thanks!

31. OpenSessame

Mind if i tag you for other questions?

32. mathstudent55

45.7?

33. mathstudent55

Not at all.

34. OpenSessame

Thanks:)

35. mathstudent55

wlcm