Find angle B in circle. Angle B rests on inner side of outer line of circle.

[DrGore]

Okay, that's a sorta confusing title but I'm tired and can't think of anything better right now.


I know that the length of the arc between angle B and the 90-degree angle on the left side of the image is 160. 360-(100+90). But after that, I'm not sure what to do really.

 

[Dr.Peterson]

Okay, that's a sorta confusing title but I'm tired and can't think of anything better right now.
View attachment 9305

I know that the length of the arc between angle B and the 90-degree angle on the left side of the image is 160. 360-(100+90). But after that, I'm not sure what to do really.

Surely there was some sort of instruction given in words. I can assume that the dot in the middle is the center of the circle, and the ray is meant to be tangent to the circle (though it doesn't look quite right). But we shouldn't have to guess.

In any case, the theorem you want is #3 on this page.

Check your arithmetic, too.

 

[lev888]

Draw the radius to the vertex of the angle in question. You'll get 2 triangles. If you can calculate the angles of one of them you'll be almost there.

 

[yma16]

extend the arrow line to the other direction

Okay, that's a sorta confusing title but I'm tired and can't think of anything better right now.
View attachment 9305

I know that the length of the arc between angle B and the 90-degree angle on the left side of the image is 160. 360-(100+90). But after that, I'm not sure what to do really.

the angle formed by the new line and the secant is half of 110. a is half of 90. So you have 55+45=100. The rest is b on the arrow line, which has 180. So 55+45+b=180

 

[DrGore]

Surely there was some sort of instruction given in words. I can assume that the dot in the middle is the center of the circle, and the ray is meant to be tangent to the circle (though it doesn't look quite right). But we shouldn't have to guess.

In any case, the theorem you want is #3 on this page.

Check your arithmetic, too.

Thank you very much! I figured it out! I seem to have a lot of problems cutting through some of the "clutter" of visual math problems like this, at least in geometry. Might you have any tips on how to better do that?

Draw the radius to the vertex of the angle in question. You'll get 2 triangles. If you can calculate the angles of one of them you'll be almost there.

the angle formed by the new line and the secant is half of 110. a is half of 90. So you have 55+45=100. The rest is b on the arrow line, which has 180. So 55+45+b=180

Also thank both of you peoples as well!

 

[Dr.Peterson]

Thank you very much! I figured it out! I seem to have a lot of problems cutting through some of the "clutter" of visual math problems like this, at least in geometry. Might you have any tips on how to better do that?

First, perhaps you noticed that what the others did amounted to (a) a derivation of the formula I referred you to, and (b) a use of the same formula in a different place. There are often multiple ways to approach a problem, which can be scary, but should really be reassuring!

Second, you had a very good start; I presume you marked your drawing with the extra arc measure you found. (Your arithmetic had the right answer, but used a miscopied number so the work you showed was wrong, which misled me.) That is the first step to "cutting clutter": find anything you can immediately derive from what is given, and add it to the picture.

A second step can be, as I suggested in a previous thread, to ignore irrelevant parts. Here, the two radii might be ignored once you've marked the arc as 90 degrees, so you might recopy the figure without them. That can literally remove clutter. (I don't usually do that, because I can't be sure something isn't needed, but it can help.)

The other thing I suggest is that, in addition to seeing what you can do with what is given, you also look at the goal and think about how you might reach it. In this case, it was to find an angle between a chord and a tangent, so your mind should immediately go to the theorem I pointed out. If it doesn't, it might go to one of the ideas the others suggested! The important thing is to have something you are aiming toward. Then take whatever steps will head you in that direction.

I compare this with how you'd find your way back to civilization if someone dropped you in the middle of a wilderness. You'd first check your pockets to find what tools you have that might be useful, and look around to find out where you are and what's available (maybe a tall tree to climb?). Then you'd think about where you are headed -- maybe you know that anyone nearby is more likely to live along a river than on a random mountain top, so you figure you should head downstream. Then you just take it step by step, hoping at each step to discover something new that might help toward the goal. Just keep moving (and keep your mind aware, so you move reasonably).

 

[DrGore]

First, perhaps you noticed that what the others did amounted to (a) a derivation of the formula I referred you to, and (b) a use of the same formula in a different place. There are often multiple ways to approach a problem, which can be scary, but should really be reassuring!

Second, you had a very good start; I presume you marked your drawing with the extra arc measure you found. (Your arithmetic had the right answer, but used a miscopied number so the work you showed was wrong, which misled me.) That is the first step to "cutting clutter": find anything you can immediately derive from what is given, and add it to the picture.

A second step can be, as I suggested in a previous thread, to ignore irrelevant parts. Here, the two radii might be ignored once you've marked the arc as 90 degrees, so you might recopy the figure without them. That can literally remove clutter. (I don't usually do that, because I can't be sure something isn't needed, but it can help.)

The other thing I suggest is that, in addition to seeing what you can do with what is given, you also look at the goal and think about how you might reach it. In this case, it was to find an angle between a chord and a tangent, so your mind should immediately go to the theorem I pointed out. If it doesn't, it might go to one of the ideas the others suggested! The important thing is to have something you are aiming toward. Then take whatever steps will head you in that direction.

I compare this with how you'd find your way back to civilization if someone dropped you in the middle of a wilderness. You'd first check your pockets to find what tools you have that might be useful, and look around to find out where you are and what's available (maybe a tall tree to climb?). Then you'd think about where you are headed -- maybe you know that anyone nearby is more likely to live along a river than on a random mountain top, so you figure you should head downstream. Then you just take it step by step, hoping at each step to discover something new that might help toward the goal. Just keep moving (and keep your mind aware, so you move reasonably).

Wow! Thank you for the very detailed post!
I think I've had the idea of writing a problem down suggested too me before but since I'm, at least at this point, doing it online I never really have. I guess that'll probably be a good first step for me. Thank you very much once more Peterson! You are very helpful person!