I see that I have forgotten a lot more about geometry than what I have forgotten about algebra, trigonometry and even calculus. Thanks John. Your videos are always interesting and instructive.
In fact, there are two ways to measure a circular arc : by its length (circle segment) or by its centre angle. Here, the question "find the arc" was unclear and that’s not good for a mathematician
That's cool. I've done some geometry about 44 years ago. Of course, I forgot the algebra that goes with it. I'm curious, how would I find the diameter (or radius) of a circle using just a measurement of a chord going across just a rather small arc of it? Thanks
The problem, as you have stated it, has insufficient information for a solution. Explanation: the chord has two end-points. There are an infinite number of circles that can go through those two end-points.
You'd need the angle formed at the centre by the radii to the two ends of the chord. Given that information... (length of chord/2) ÷ (sin(angle at centre)/2) ... will get you the radius.
Dammit, I wish that diagram was labelled. But okay: The inscribed angle = 90 − 47 = 43° The angle at the centre (let's call it c) is ½ the inscribed angle ∴ c = 43 × 2 = 86° Edit. Oops! I meant to say, of course that the inscribed angle is ½ the angle at the centre. I got the maths right, but evidently I suck at prose.
It seems to me that the formula at the 9:10 minute point needs to be proven. That would be the real point of this exercise. I have never seen it and it does not seem intuitive.
I had drawn another radius out to G to make an isosceles triangle up top, finding that the two 43 degree angles summed to 86, meaning that angle AOG was 94 and thus the angle of arc BOG would also be 86 to add up to 180. I think I accidentally made a basic proof of that chord inscription rule lmao
I'm going to Milky Lane... for waffles. Dude, you wasted 8 minutes just to get to the third angle of the triangle. Complete waste of my time. Speed it up by an order of magnitude.
I see that I have forgotten a lot more about geometry than what I have forgotten about algebra, trigonometry and even calculus. Thanks John. Your videos are always interesting and instructive.
Curious why you measure the arc in degrees? Is that what the angle would be if drawn from the centre?
Is it the fraction of 360°?
In fact, there are two ways to measure a circular arc : by its length (circle segment) or by its centre angle. Here, the question "find the arc" was unclear and that’s not good for a mathematician
That's cool. I've done some geometry about 44 years ago. Of course, I forgot the algebra that goes with it.
I'm curious, how would I find the diameter (or radius) of a circle using just a measurement of a chord going across just a rather small arc of it?
Thanks
The problem, as you have stated it, has insufficient information for a solution. Explanation: the chord has two end-points. There are an infinite number of circles that can go through those two end-points.
You'd need the angle formed at the centre by the radii to the two ends of the chord. Given that information...
(length of chord/2) ÷ (sin(angle at centre)/2)
... will get you the radius.
@@dazartingstall6680
Wow, thanks!
Dammit, I wish that diagram was labelled. But okay:
The inscribed angle = 90 − 47 = 43°
The angle at the centre (let's call it c) is ½ the inscribed angle
∴ c = 43 × 2 = 86°
Edit. Oops! I meant to say, of course that the inscribed angle is ½ the angle at the centre. I got the maths right, but evidently I suck at prose.
Got 86 opp angle of 47 is 43. Sum is 90.
43 x 2 = 86.
Thanks for the fun.
Thank you
It seems to me that the formula at the 9:10 minute point needs to be proven. That would be the real point of this exercise. I have never seen it and it does not seem intuitive.
I had drawn another radius out to G to make an isosceles triangle up top, finding that the two 43 degree angles summed to 86, meaning that angle AOG was 94 and thus the angle of arc BOG would also be 86 to add up to 180. I think I accidentally made a basic proof of that chord inscription rule lmao
43/90 * (di*pi) = length measure
86
3.14 × the square of radius / 4...
I'm going to Milky Lane... for waffles.
Dude, you wasted 8 minutes just to get to the third angle of the triangle. Complete waste of my time. Speed it up by an order of magnitude.
Eight minutes‽ OMG the sheer mental torture of it all!
Stall ebong jal lagbe.
ez
Gee, I’m a tree!
No way would I subscribe to this channel. So much talking about absolutely nothing, and its all deliberate for monetary gains.