pka disagrees with a valid method

[pka]

In this problem, I need to prove angle AOB = 2 angle ACB (2y). View attachment 27547

I almost never reply if it requires completing someone else's proof.
But in this case the suggested proof is so ridiculous as to cry out for a correction.
1) \(m(\widehat{AB})=m(\angle AOB)\); the central angle theorem.
2) \(m(\widehat{AB})=2m(\angle ACB)\); the inscribed angle theorem.
3) \(\therefore~,~ m(\angle AOB)=2y^o\)

 

[Deleted member 4993]

I almost never reply if it requires completing someone else's proof.
But in this case the suggested proof is so ridiculous as to cry out for a correction.
1) \(m(\widehat{AB})=m(\angle AOB)\); the central angle theorem.
2) \(m(\widehat{AB})=2m(\angle ACB)\); the inscribed angle theorem.
3) \(\therefore~,~ m(\angle AOB)=2y^o\)

OP did NOT ask for a proof - s/he asked for a clarification in a "given" proof:

This is the answer's working. I understand up until it introduces a 2x in the third line. Where did this come from?

. "Ridiculous" or not - the answer was correct (not pithy).

 

[Dr.Peterson]

I almost never reply if it requires completing someone else's proof.
But in this case the suggested proof is so ridiculous as to cry out for a correction.
1) \(m(\widehat{AB})=m(\angle AOB)\); the central angle theorem.
2) \(m(\widehat{AB})=2m(\angle ACB)\); the inscribed angle theorem.
3) \(\therefore~,~ m(\angle AOB)=2y^o\)

The problem amounts to a statement of the inscribed angle theorem, and the provided answer is a valid proof of that theorem. Presumably the context does not include having that theorem already established.

When I answer a question, I try to deduce the context (since it is rarely stated explicitly) and answer accordingly. If something would be ridiculous in the context I first imagine, I assume I am thinking incorrectly, and reconsider the context. This is an essential part of helping people.

 

[pka]

In this problem, I need to prove angle AOB = 2 angle ACB (2y). This is the answer's working. I understand up until it introduces a 2x in the third line. Where did this come from?
angle OBC = x+y (triangle OCB is isosceles)
angle COB = 180-2(x+y)
angle AOB = 180-2x-(180-2(x+y))
therefore angle AOB = 2y

OP did NOT ask for a proof - s/he asked for a clarification in a "given" proof:
. "Ridiculous" or not - the answer was correct (not pithy).

Prof Khan. I know you read carefully, so what does the OP mean there?
Moreover, the title of the thread is Angles in a circle.
Surely that suggests using theorems about angles in circles, does it not?

 

[mmm4444bot]

I think the meaning of that thread is clear enough. Sunflower had asked a direct question about someone else's workings, and Prof Khan provided Sunflower with a direct response. If pka desires further clarification, then I think he ought to initiate a private conversation with Sunflower.

This is a tutoring forum. It is not a tutor's position to complain about or ridicule valid course material in students' threads that the tutor happens to personally dislike (eg: vocabulary, symbolism, units of measurement, approaches).

If any member wishes to introduce a personal agenda related to specific assignments appearing in the forum, then they may express their personal preferences in their own threads on the Math Odds & Ends board. Such commentary/complaining is off-topic, in students' threads.

?

 

[JeffM]

I think the meaning of that thread is clear enough. Sunflower had asked a direct question about someone else's workings, and Prof Khan provided Sunflower with a direct response. If pka desires further clarification, then I think he ought to initiate a private conversation with Sunflower.

This is a tutoring forum. It is not a tutor's position to complain about or ridicule valid course material in students' threads that the tutor happens to personally dislike (eg: vocabulary, symbolism, units of measurement, approaches).

If any member wishes to introduce a personal agenda related to specific assignments appearing in the forum, then they may express their personal preferences in their own threads on the Math Odds & Ends board. Such commentary/complaining is off-topic, in students' threads.

?

I cannot quite agree with this general position. Sometimes students are confused because their materials are wrong (usually due to a typo) or unnecessarily obscure. If a student’s failure to understand arises for either reason, it seems quite appropriate to me to give the student confidence in their own thought processes by being direct about where and how teaching materials are at fault. Learning math is hard for most students. Pretending that teachers are always correct and clear undercuts the development of students’ critical thought.

This specific case lies outside that concern. Here there was no error. Instead, we have a different issue, namely that discussing proofs requires knowing what in fact we cannot know, namely what axioms and theorems are available to the student.