OpenSessame
In circle O, m<R = 23. Find m<O. (The figure is not drawn to scale.)
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Directrix
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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.
Directrix
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The measure of an inscribed angle is how related to its intercepted arc?
OpenSessame
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I understand the theorem but how do find the length?
Directrix
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Read the part of the attachment that says that the measure of the inscribed angle is ...... ? What comes next?
OpenSessame
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1/2 the measue of the arc
OpenSessame
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so multply it by two?
Directrix
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Yes.
So if angle R is 23, what is the measure of arc NQ ?
OpenSessame
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do its 46?
Directrix
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Yes.
Next, do you see that central angle O cuts off the same arc that angle R did?
OpenSessame
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Right so 23?
Directrix
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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?
OpenSessame
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1/2
Directrix
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No, that was the inscribed angle. We're talking central angles.
OpenSessame
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I have no idea...
Directrix
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Read this.
OpenSessame
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Okay i did..
OpenSessame
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It is the arc!
OpenSessame
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So the Angle is 46!
Directrix
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That is correct.
OpenSessame
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THANK YOU SOO MUCH!
Directrix
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You are welcome.
Directrix
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Yes.
OpenSessame
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Because they are congruent right?
Directrix
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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.
OpenSessame
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Okay, well thank you a lot!
Directrix
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We have done one like that.
Directrix
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Here's the theorem you need. ^^
Directrix
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So, what is the equation you would write to solve the equation.
OpenSessame
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Alright! I got it from here! Thanks man!
OpenSessame
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X^2=5(12+5)
Directrix
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Very good.
Directrix
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X^2 = ?
OpenSessame
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9.2?
OpenSessame
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85
OpenSessame
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Would it be 9.2 or 85???
Directrix
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x^2 = 85
x = 9.2? Yes.
OpenSessame
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Okay:) thanks!
Directrix
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I'll look for you online when I'm on. I enjoyed working with you.
OpenSessame
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Thanks same with you!