# Geometry problem with arcs in a triangle

• albertoita
In summary, the conversation is about solving a geometric exercise involving circular arcs and the point S. The participants discuss using the formula ##s = r\theta## and drawing lines to find the solution. One participant requests a detailed explanation and drawing, but the other declines, stating that they have already provided enough assistance. The conversation ends with a reminder that the forum does not provide solutions to schoolwork questions.

#### albertoita

Thread moved from the technical forums to the schoolwork forums
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.

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

PeroK
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

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.

ok thanks again still

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

PeroK and SammyS
@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.

@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.

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

PeroK