Geometry problem with arcs in a triangle

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.
  • #1
albertoita
8
1
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.
WhatsApp Image 2023-01-12 at 20.50.52.jpeg
 
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  • #2
Is this homework?
 
  • #3
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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  • #4
PeroK said:
Is this homework?
theoretically it could be but only for my pleassure
 
  • #5
PeroK said:
Is this homework?
could you find the answer with explanation
 
  • #6
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?
 
  • #7
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
 
  • #8
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!
 
  • #9
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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Related to Geometry problem with arcs in a triangle

What is an arc in the context of a triangle?

An arc in the context of a triangle typically refers to a segment of a circle's circumference that is defined by two points on the triangle. This could be an arc of the circumcircle (the circle that passes through all three vertices of the triangle) or an arc of an incircle or excircle (circles that are tangent to the sides of the triangle).

How do you find the length of an arc within a triangle?

The length of an arc can be found using the formula \( L = r \theta \), where \( L \) is the length of the arc, \( r \) is the radius of the circle, and \( \theta \) is the central angle in radians that subtends the arc. If the angle is given in degrees, it must be converted to radians first by multiplying by \(\pi / 180\).

What is the significance of the circumcircle in solving geometry problems involving arcs in a triangle?

The circumcircle is significant because it passes through all three vertices of the triangle, making it a useful tool for solving problems involving arcs. Properties of the circumcircle, such as its radius (circumradius) and the angles subtended by arcs, can simplify the calculations and provide insights into the relationships between different parts of the triangle.

How can the properties of inscribed angles help in solving problems with arcs in a triangle?

Inscribed angles are angles formed by two chords in a circle that share an endpoint. The measure of an inscribed angle is half the measure of the arc it intercepts. This property can be used to find unknown angles and arc lengths in problems involving arcs in a triangle, especially when dealing with the circumcircle.

What role do special points like the incenter and circumcenter play in geometry problems with arcs in a triangle?

The incenter is the point where the angle bisectors of a triangle intersect and is the center of the incircle, which is tangent to all three sides of the triangle. The circumcenter is the point where the perpendicular bisectors of the sides intersect and is the center of the circumcircle. These points help determine the radii of the respective circles, which are crucial for calculating arc lengths and understanding the geometric relationships within the triangle.

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