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OpenSessame

  • 2 years ago

In circle O, m<R = 23. Find m<O. (The figure is not drawn to scale.)

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  1. Directrix
    • 2 years ago
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    Angle R is an inscribed angle of a circle. Use the attached theorem to get the measure of the arc it cuts off. The intercepted arc is in blue.

  2. Directrix
    • 2 years ago
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    The measure of an inscribed angle is how related to its intercepted arc?

  3. OpenSessame
    • 2 years ago
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    I understand the theorem but how do find the length?

  4. Directrix
    • 2 years ago
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    Read the part of the attachment that says that the measure of the inscribed angle is ...... ? What comes next?

  5. OpenSessame
    • 2 years ago
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    1/2 the measue of the arc

  6. OpenSessame
    • 2 years ago
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    so multply it by two?

  7. Directrix
    • 2 years ago
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    Yes. So if angle R is 23, what is the measure of arc NQ ?

  8. OpenSessame
    • 2 years ago
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    do its 46?

  9. Directrix
    • 2 years ago
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    Yes. Next, do you see that central angle O cuts off the same arc that angle R did?

  10. OpenSessame
    • 2 years ago
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    Right so 23?

  11. Directrix
    • 2 years ago
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    No, the central angle is not 23. On the previous problem, what did we say is the measure of the central angle of a circle in relation to its intercepted arc?

  12. OpenSessame
    • 2 years ago
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    1/2

  13. Directrix
    • 2 years ago
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    No, that was the inscribed angle. We're talking central angles.

  14. OpenSessame
    • 2 years ago
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    I have no idea...

  15. Directrix
    • 2 years ago
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    Read this.

  16. OpenSessame
    • 2 years ago
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    Okay i did..

  17. OpenSessame
    • 2 years ago
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    It is the arc!

  18. OpenSessame
    • 2 years ago
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    So the Angle is 46!

  19. Directrix
    • 2 years ago
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    That is correct.

  20. OpenSessame
    • 2 years ago
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    THANK YOU SOO MUCH!

  21. Directrix
    • 2 years ago
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    You are welcome.

  22. OpenSessame
    • 2 years ago
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    https://study.ashworthcollege.edu/access/content/group/45b8c516-1008-46d7-aa1d-bb9b62c786ff/geometry_exam_12_files/mc003-1.jpg For this wouldnt the X angle be 77?

  23. Directrix
    • 2 years ago
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    Yes.

  24. OpenSessame
    • 2 years ago
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    Because they are congruent right?

  25. OpenSessame
    • 2 years ago
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    https://study.ashworthcollege.edu/access/content/group/45b8c516-1008-46d7-aa1d-bb9b62c786ff/geometry_exam_12_files/mc012-1.jpg This is confusing me again...

  26. Directrix
    • 2 years ago
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    There is a little bit more to it. You don't know that the angles are congruent right off the bat. Look at the two congruent chords of the circle that go with the arcs cut off by the two central angles. Because in a circle, congruent chords have congruent arcs and the two central angles cut off congruent arcs, their measures are the same.

  27. OpenSessame
    • 2 years ago
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    Okay, well thank you a lot!

  28. Directrix
    • 2 years ago
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    We have done one like that.

  29. Directrix
    • 2 years ago
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    Here's the theorem you need. ^^

  30. Directrix
    • 2 years ago
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    So, what is the equation you would write to solve the equation.

  31. OpenSessame
    • 2 years ago
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    Alright! I got it from here! Thanks man!

  32. OpenSessame
    • 2 years ago
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    X^2=5(12+5)

  33. Directrix
    • 2 years ago
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    Very good.

  34. Directrix
    • 2 years ago
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    X^2 = ?

  35. OpenSessame
    • 2 years ago
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    9.2?

  36. OpenSessame
    • 2 years ago
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    85

  37. OpenSessame
    • 2 years ago
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    Would it be 9.2 or 85???

  38. Directrix
    • 2 years ago
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    x^2 = 85 x = 9.2? Yes.

  39. OpenSessame
    • 2 years ago
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    Okay:) thanks!

  40. Directrix
    • 2 years ago
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    I'll look for you online when I'm on. I enjoyed working with you.

  41. OpenSessame
    • 2 years ago
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    Thanks same with you!

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