chord in a circle

[logistic_guy]

The radius of circle \(\displaystyle O\) is \(\displaystyle 13 \ \text{mm}\). The length of chord \(\displaystyle \overline{PQ}\) is \(\displaystyle 10 \ \text{mm}\). Find the distance from chord \(\displaystyle \overline{PQ}\) to the center, \(\displaystyle O\).

 

[The Highlander]

The radius of circle \(\displaystyle O\) is \(\displaystyle 13 \ \text{mm}\). The length of chord \(\displaystyle \overline{PQ}\) is \(\displaystyle 10 \ \text{mm}\). Find the distance from chord \(\displaystyle \overline{PQ}\) to the center, \(\displaystyle O\).
View attachment 39725

The answer is (quite simply) 12 mm. Can you see why?


NB: Given that PQ is 10 mm, it doesn't look like the distance from the chord to the centre
is 12 mm but that's because your diagram is extremely inaccurate; it ought to look like this:

 

[logistic_guy]

The answer is (quite simply) 12 mm. Can you see why?
View attachment 39728

NB: Given that PQ is 10 mm, it doesn't look like the distance from the chord to the centre
is 12 mm but that's because your diagram is extremely inaccurate; it ought to look like this:

Your sketch is very wrong. And that is not the right way to learn Geometry. If you wanna learn Geometry properly, you will have to follow all of my previous Geometry's problems as well as my future ones.

In the future Geometry's problems, try to solve them with a pencil and paper without any help. Then, you will have to wait until I reveal my answer. After that, you can compare your answer with my answer.

In this manner, you will be better than Aion in no time. Of course, you will take a lot of time to master the subject, but you will enjoy every second of it.

 

[The Highlander]

Your sketch is very wrong. And that is not the right way to learn Geometry. If you wanna learn Geometry properly, you will have to follow all of my previous Geometry's problems as well as my future ones.

In the future Geometry's problems, try to solve them with a pencil and paper without any help. Then, you will have to wait until I reveal my answer. After that, you can compare your answer with my answer.

In this manner, you will be better than Aion in no time. Of course, you will take a lot of time to master the subject, but you will enjoy every second of it.

What an absolute, feckin plonker!!!

​

 

[logistic_guy]

What an absolute, feckin plonker!!!

View attachment 39736
View attachment 39732​

It seems that you don't want to listen to the advice given to you by someone who has more knowledge than you because you think that you are better than him!

If you think that you are more superior because you have been teaching for more than \(\displaystyle \textcolor{darkblue}{\bold{30}}\) years, ask yourself, who did you teach and what did you teach?

High school students \(\displaystyle \longrightarrow\) Basics?

Therefore, your math experience is very limited.

Ask yourself why you don't understand abstract mathematics or differential geometry if you want to understand why spending even \(\displaystyle \textcolor{indigo}{\bold{100}}\) years in teaching the basics is not even considered a little knowledge in this very wide world of mathematics.

\(\displaystyle \textcolor{red}{\bold{FYI}}\). It is true that most of the problems I posted I have never solved before, but I know how to solve every one of them. I just post and solve them online to entertain myself, practise latex, and annoy some people like you.

You can think of this forum as my huge scratch paper which allows me to share my solving strategy with the world.

 

[logistic_guy]

The radius of circle \(\displaystyle O\) is \(\displaystyle 13 \ \text{mm}\). The length of chord \(\displaystyle \overline{PQ}\) is \(\displaystyle 10 \ \text{mm}\). Find the distance from chord \(\displaystyle \overline{PQ}\) to the center, \(\displaystyle O\).
View attachment 39725

Draw a perpendicular line from point \(\displaystyle O\) to the segment \(\displaystyle \overline{PQ}\). Since this line is the perpendicular bisector of segment \(\displaystyle \overline{PQ}\), we can sketch a right triangle with two known segments.

Then,

Find the distance from chord \(\displaystyle \overline{PQ}\) to the center, \(\displaystyle O\).

\(\displaystyle D = \sqrt{r^2 - \left(\frac{\overline{PQ}}{2}\right)^2} = \sqrt{13^2 - \left(\frac{10}{2}\right)^2} = \textcolor{blue}{12}\)

 

[The Highlander]

Draw a perpendicular line from point \(\displaystyle O\) to the segment \(\displaystyle \overline{PQ}\). Since this line is the perpendicular bisector of segment \(\displaystyle \overline{PQ}\), we can sketch a right triangle with two known segments.
Then,
\(\displaystyle D = \sqrt{r^2 - \left(\frac{\overline{PQ}}{2}\right)^2} = \sqrt{13^2 - \left(\frac{10}{2}\right)^2} = \textcolor{blue}{12}\)

I see you finally managed to get the right answer (same as mine) after your laborious treatise using the Geometrical fact that I, with my humble understanding of Maths, provided for you (here) in an attempt to extend your (already 'encyclopaedic' ) knowledge!
(Though you do seem to have difficulty in absorbing new concepts; probably due to your extreme arrogance and complete lack of empathy! )

Your sketch is very wrong. And that is not the right way to learn Geometry. If you wanna learn Geometry properly, you will have to follow all of my previous Geometry's problems as well as my future ones.

In the future Geometry's problems, try to solve them with a pencil and paper without any help. Then, you will have to wait until I reveal my answer. After that, you can compare your answer with my answer.

In this manner, you will be better than Aion in no time. Of course, you will take a lot of time to master the subject, but you will enjoy every second of it.

It's a Pythagorean triple, you dimwit, you don't need "pencil and paper" to get the answer; you can see immediately what the answer is if you have any understanding of (Basic, lol) Geometry!
Just as my completely accurate drawing (not "sketch"), which was constructed (precisely) in Desmos, quite clearly illustrated for anyone with half a brain.

It seems that you don't want to listen to the advice given to you by someone who has more knowledge than you because you think that you are better than him!

If you think that you are more superior because you have been teaching for more than \(\displaystyle \textcolor{darkblue}{\bold{30}}\) years, ask yourself, who did you teach and what did you teach?

High school students \(\displaystyle \longrightarrow\) Basics?

Therefore, your math experience is very limited.

Ask yourself why you don't understand abstract mathematics or differential geometry if you want to understand why spending even \(\displaystyle \textcolor{indigo}{\bold{100}}\) years in teaching the basics is not even considered a little knowledge in this very wide world of mathematics.

\(\displaystyle \textcolor{red}{\bold{FYI}}\). It is true that most of the problems I posted I have never solved before, but I know how to solve every one of them. I just post and solve them online to entertain myself, practise latex, and annoy some people like you.

You can think of this forum as my huge scratch paper which allows me to share my solving strategy with the world.

I (like you probably did yourself) had fully expected that, once you reached 2,000 posts, you would attain the "Elite" status that you are. clearly. so desperately striving towards. How disappointing it must have been for you to discover that 2,000 posts was not the benchmark for promotion to that exalted position!
Who knows? Maybe there is some other criterion that needs to be met to be raised to that level; perhaps the agreement of your peers (or, rather, your betters) needs to be sought by the owner or a moderator beforehand?

No doubt you will continue to stuff the forum with your crap regardless in the hope that, eventually, you will be marked as an "Elite" member. Much good it will do you as there will still be no one who has an iota of respect for you (or your ramblings) and, if the forum ever does come "back to life", the first thing on the agenda will be to boot your arse out of it and remove all the rubbish you have been allowed to post during this hiatus.

However, I (like so many others) have lost interest in the drivel you post and have completely lost patience with your arrogant self-aggrandizement so I am now putting you on "Ignore".

Don't bother to Reply; I won't see it!