Geometry problem with arcs in a triangle

AI Thread Summary
The discussion revolves around a geometry problem involving circular arcs within a triangle, specifically demonstrating that the sixth arc returns to the starting point S and that the total length of the six arcs equals the length of two dotted arcs. Participants express frustration over the lack of a clear solution, with one user repeatedly requesting a detailed explanation. Another user mentions using the formula for arc length but finds it unhelpful. Ultimately, the thread is closed for moderation, emphasizing that solutions to schoolwork-type questions are the responsibility of the individual. The conversation highlights the challenges of collaborative problem-solving in mathematics.
albertoita
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In the figure, the point S is located inside the section FE.
Starting from S, as indicated in the figure, six circular arcs are drawn step by step around
arcs around A, C, B, A, C, B are drawn.
Show that the sixth arc leads back to S and that the six arcs together are then exactly as long as the two dotted arcs together.
WhatsApp Image 2023-01-12 at 20.50.52.jpeg
 
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Is this homework?
 
no it,s an excercise I tried to do that my friend gave me 2 months ago and I still can't find an answer
 
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PeroK said:
Is this homework?
theoretically it could be but only for my pleassure
 
PeroK said:
Is this homework?
could you find the answer with explanation
 
albertoita said:
could you find the answer with explanation
I don't know. My first thought is to use ##s = r\theta##, where ##s## is arc length subtended by angle ##\theta## on a circle of radius ##r##.

Have you tried that?
 
PeroK said:
I don't know. My first thought is to use ##s = r\theta##, where ##s## is arc length subtended by angle ##\theta## on a circle of radius ##r##.

Have you tried that?
I've tried that.Didn't work.Could you try to like find a long explanation with math and words
 
albertoita said:
I've tried that.Didn't work.Could you try to like find a long explanation with math and words
It's nearly my bedtime!
 
Oh ok could you maybe try tomorrow find a long explanation and right explanation
 
  • #10
albertoita said:
Oh ok could you maybe try tomorrow find a long explanation and right explanation
Don't worry. There are more able mathematicians than me on here.
 
  • #11
ok thanks again still
 
  • #12
Problem seems trivial to me. Took me no time at all to figure it out and then quite a bit more time to draw this, so you can see it. Just to make sure it's clear, my "conclusion Z" follows from the geometry/arithmetic without ever drawing line 8

1673559767523.png
 
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  • #13
@albertoita I got a PM from you asking for more detail but the PM is closed to new posts so I can't answer you there. In any case, just follow the drawing of lines 1, 2, 3, 4, 5, 6, and 7 in that order. Clearly a = a1 = a2 = a3 and everything else is trivial arithmetic.
 
  • #14
@albertoita I have now received THREE additional PM's from you asking for a complete and detailed explanation, all drawn out with great precision. Please STOP sending me these PM's.

I have spent as much time on this as I feel is necessary and I am not going to do anything more. I did you the favor of posting a complete solution in post #12. That's it.
 
  • #15
phinds said:
@albertoita I got a PM from you asking for more detail but the PM is closed to new posts so I can't answer you there. In any case, just follow the drawing of lines 1, 2, 3, 4, 5, 6, and 7 in that order. Clearly a = a1 = a2 = a3 and everything else is trivial arithmetic.
I need to have a perfect solution .Everything must be shown perfectly
phinds said:
@albertoita I have now received THREE additional PM's from you asking for a complete and detailed explanation, all drawn out with great precision. Please STOP sending me these PM's.

I have spent as much time on this as I feel is necessary and I am not going to do anything more. I did you the favor of posting a complete solution in post #12. That's it.
i don’t understand ur drawing
 
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  • #16
Thread is closed for Moderation...
 
  • #17
albertoita said:
I need to have a perfect solution .Everything must be shown perfectly
We do not provide solutions to schoolwork-type questions. That is your task, not ours. The thread will remain closed -- check your PMs.
 
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