Impossible?? Theorem 10:13 and finding arcs

[iwinnlots]

Ok, now work with me here. I am only in the 10th grade. I am in Geometry class and we are working on circles. We come across theorem 10.13 about X=1/2 (a+b) you know the deal... but i had the bright idea to ask my teacher if you can solve those other two arcs with the info given. What i have gotten so far is just a little bit but maybe someone else can help...

I thought that if you draw a line in that would be the diameter you would get an inscribed angle. That inscribed angle would tell us that the arc that it creates is going to be 2X. So now you know that arc... You take that arc + the arc you already solved for and you get a number, X. take 180-X and you will get your unknown arc... add all those together and you get 180. Then on the other semicircle you repeat the same process... sorry if i confused anyone but i am completely lost on this one.


I have added a simple diagram that i found on the internet that sums up the base problem... any help would be great

 

[stapel]

We come across theorem 10.13 about X=1/2 (a+b) you know the deal...

Um... No, actually; we don't. :shock:

We're not in your class and we don't have your book. You'll need to tell us what "Theorem 10:13" says, or to what "X=1/2(a+b)" refers, and how either relates to the exercise at hand. Also, which are "the other arcs", is "S" the center of the circle, and what other information was provided for the exercise?

Please be clear and complete. Thank you!

Eliz.

 

[Mrspi]

Ok, now work with me here. I am only in the 10th grade. I am in Geometry class and we are working on circles. We come across theorem 10.13 about X=1/2 (a+b) you know the deal... but i had the bright idea to ask my teacher if you can solve those other two arcs with the info given. What i have gotten so far is just a little bit but maybe someone else can help...

I thought that if you draw a line in that would be the diameter you would get an inscribed angle. That inscribed angle would tell us that the arc that it creates is going to be 2X. So now you know that arc... You take that arc + the arc you already solved for and you get a number, X. take 180-X and you will get your unknown arc... add all those together and you get 180. Then on the other semicircle you repeat the same process... sorry if i confused anyone but i am completely lost on this one.


I have added a simple diagram that i found on the internet that sums up the base problem... any help would be great

I'll take a guess that "theorem 10.13" says something like this:

The measure of the angle formed by two chords intersecting inside a circle (such as <1 in your diagram) is equal to 1/2 times the sum of the two intercepted arcs. Or, m<1 = (1/2)*[m(arc AB) + m(arc CD)]

Here's a hint on how to prove this theorem. Draw segment AD. Now, you have created a triangle AED, and <1 is an exterior angle for this triangle. Remember (you should have proved this theorem earlier) that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. Thus,

m<1 = m<EAD + m<EDA

Now, <EAD is an inscribed angle with arc CD as its intercepted arc, and <EDA is an inscribed angle with arc AB as its intercepted arc. Knowing the relationship between the measure of an inscribed angle and the measure of its intercepted arc, you should be able to complete the proof of your theorem without too much trouble.

And....geometry is most often studied by folks who are "only in 10th grade."

 

[iwinnlots]

ok so can u throw some numbers in there and prove your theorem? please and can you show a example drawing

 

[iwinnlots]

Can someone draw up an example and please throw in some numbers so i can see it proved. :roll:

 

[stapel]

ok so can u throw some numbers in there and prove your theorem? please and can you show a example drawing

You've been given a hint as to how to proceed. Where are you stuck?

Note: The volunteers really can't teach lessons here. If you are needing proofs, worked examples, and explanations (that is, lessons), you might want to consider taking a class or hiring a qualified local tutor who can provide you with the private classes you seek.

Eliz.

 

[Mrspi]

ok so can u throw some numbers in there and prove your theorem? please and can you show a example drawing

I'm really sorry...I thought this was YOUR theorem that you wanted to prove. So, I gave you a hint about how to do that.

Please show us what you've done to try to prove this theorem. Generally speaking, we don't "throw numbers" into a geometric situation if we are trying to prove that something is true IN GENERAL.

I guess I misunderstood what you are trying to do here....

Please repost your specific problem, and show us what you've tried to do. Then maybe we'll have a better idea of how to help you.