Geometry problem with arcs in a triangle

[albertoita]

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.

 

[PeroK]

Is this homework?

 

[albertoita]

no it,s an exercise I tried to do that my friend gave me 2 months ago and I still can't find an answer

 

[albertoita]

Is this homework?

theoretically it could be but only for my pleassure

 

[albertoita]

Is this homework?

could you find the answer with explanation

 

[PeroK]

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?

 

[albertoita]

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

 

[PeroK]

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!

 

[albertoita]

Oh ok could you maybe try tomorrow find a long explanation and right explanation

 

[PeroK]

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.

 

[albertoita]

ok thanks again still

 

[phinds]

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

 

[phinds]

@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.

 

[phinds]

@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.

 

[albertoita]

@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

@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

 

[berkeman]

Thread is closed for Moderation...

 

[berkeman]

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.