## OpenSessame 2 years ago In circle O, m<R = 23. Find m<O. (The figure is not drawn to scale.)

1. OpenSessame
2. Directrix

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.

3. Directrix

The measure of an inscribed angle is how related to its intercepted arc?

4. OpenSessame

I understand the theorem but how do find the length?

5. Directrix

Read the part of the attachment that says that the measure of the inscribed angle is ...... ? What comes next?

6. OpenSessame

1/2 the measue of the arc

7. OpenSessame

so multply it by two?

8. Directrix

Yes. So if angle R is 23, what is the measure of arc NQ ?

9. OpenSessame

do its 46?

10. Directrix

Yes. Next, do you see that central angle O cuts off the same arc that angle R did?

11. OpenSessame

Right so 23?

12. Directrix

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?

13. OpenSessame

1/2

14. Directrix

No, that was the inscribed angle. We're talking central angles.

15. OpenSessame

I have no idea...

16. Directrix

17. OpenSessame

Okay i did..

18. OpenSessame

It is the arc!

19. OpenSessame

So the Angle is 46!

20. Directrix

That is correct.

21. OpenSessame

THANK YOU SOO MUCH!

22. Directrix

You are welcome.

23. OpenSessame

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?

24. Directrix

Yes.

25. OpenSessame

Because they are congruent right?

26. OpenSessame
27. Directrix

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.

28. OpenSessame

Okay, well thank you a lot!

29. Directrix

We have done one like that.

30. Directrix

Here's the theorem you need. ^^

31. Directrix

So, what is the equation you would write to solve the equation.

32. OpenSessame

Alright! I got it from here! Thanks man!

33. OpenSessame

X^2=5(12+5)

34. Directrix

Very good.

35. Directrix

X^2 = ?

36. OpenSessame

9.2?

37. OpenSessame

85

38. OpenSessame

Would it be 9.2 or 85???

39. Directrix

x^2 = 85 x = 9.2? Yes.

40. OpenSessame

Okay:) thanks!

41. Directrix

I'll look for you online when I'm on. I enjoyed working with you.

42. OpenSessame

Thanks same with you!