Difficulty in this Olympiad problem [closed]

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Peter was cutting a pipe with an outside diameter of 20cm. When the cut was just through the wall of the pipe, it was 10 cm in length. How thick was the wall of the pipe in centimeters?




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closed as off-topic by Jyrki Lahtonen, amWhy, Jendrik Stelzner, Delta-u, Adrian Keister Aug 6 at 13:12


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Jyrki Lahtonen, amWhy, Jendrik Stelzner, Delta-u, Adrian Keister
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    You should show us what you have done so far.
    – Le Anh Dung
    Aug 6 at 6:10










  • This is from a competition from 2015: here's a link. In general it's good form to say exactly where/when the problem is from.
    – Mason
    Aug 6 at 7:07















up vote
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down vote

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enter image description here



Peter was cutting a pipe with an outside diameter of 20cm. When the cut was just through the wall of the pipe, it was 10 cm in length. How thick was the wall of the pipe in centimeters?




contest-math problem-solving




share|cite|improve this question













closed as off-topic by Jyrki Lahtonen, amWhy, Jendrik Stelzner, Delta-u, Adrian Keister Aug 6 at 13:12


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Jyrki Lahtonen, amWhy, Jendrik Stelzner, Delta-u, Adrian Keister
If this question can be reworded to fit the rules in the help center, please edit the question.








  • 1




    You should show us what you have done so far.
    – Le Anh Dung
    Aug 6 at 6:10










  • This is from a competition from 2015: here's a link. In general it's good form to say exactly where/when the problem is from.
    – Mason
    Aug 6 at 7:07













up vote
-4
down vote

favorite









up vote
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down vote

favorite











enter image description here



Peter was cutting a pipe with an outside diameter of 20cm. When the cut was just through the wall of the pipe, it was 10 cm in length. How thick was the wall of the pipe in centimeters?




contest-math problem-solving




share|cite|improve this question













enter image description here



Peter was cutting a pipe with an outside diameter of 20cm. When the cut was just through the wall of the pipe, it was 10 cm in length. How thick was the wall of the pipe in centimeters?





contest-math problem-solving





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Aug 6 at 6:59









Le Anh Dung

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asked Aug 6 at 6:03









Daniyal Bilal

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1




closed as off-topic by Jyrki Lahtonen, amWhy, Jendrik Stelzner, Delta-u, Adrian Keister Aug 6 at 13:12


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Jyrki Lahtonen, amWhy, Jendrik Stelzner, Delta-u, Adrian Keister
If this question can be reworded to fit the rules in the help center, please edit the question.




closed as off-topic by Jyrki Lahtonen, amWhy, Jendrik Stelzner, Delta-u, Adrian Keister Aug 6 at 13:12


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Jyrki Lahtonen, amWhy, Jendrik Stelzner, Delta-u, Adrian Keister
If this question can be reworded to fit the rules in the help center, please edit the question.







  • 1




    You should show us what you have done so far.
    – Le Anh Dung
    Aug 6 at 6:10










  • This is from a competition from 2015: here's a link. In general it's good form to say exactly where/when the problem is from.
    – Mason
    Aug 6 at 7:07













  • 1




    You should show us what you have done so far.
    – Le Anh Dung
    Aug 6 at 6:10










  • This is from a competition from 2015: here's a link. In general it's good form to say exactly where/when the problem is from.
    – Mason
    Aug 6 at 7:07








1




1




You should show us what you have done so far.
– Le Anh Dung
Aug 6 at 6:10




You should show us what you have done so far.
– Le Anh Dung
Aug 6 at 6:10












This is from a competition from 2015: here's a link. In general it's good form to say exactly where/when the problem is from.
– Mason
Aug 6 at 7:07





This is from a competition from 2015: here's a link. In general it's good form to say exactly where/when the problem is from.
– Mason
Aug 6 at 7:07











1 Answer
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Given that the cut is just through the wall of the pipe, that means on the outside circle of diameter 20cm, and thus radius 10cm, it has a chord of length 10cm such that the chord is also tangent to the inner circle.



If you draw that chord and draw two segments connecting either endpoint of the chord to the center of the 10cm radius circle, you get an equilateral triangle. Taking the altitude of that triangle with the base being the chord, you can find the altitude length to be equal to $5 sqrt3$. This attitude is also the radius of the inner circle as the chord is tangent to the inner circle and altitudes form right angles with the base.



Thus, the thickness of the pipe is then $10 - 5 sqrt3 = 5(2-sqrt3)$, which is choice (E).






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    1 Answer
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    1 Answer
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    active

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    active

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    active

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    up vote
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    down vote













    Given that the cut is just through the wall of the pipe, that means on the outside circle of diameter 20cm, and thus radius 10cm, it has a chord of length 10cm such that the chord is also tangent to the inner circle.



    If you draw that chord and draw two segments connecting either endpoint of the chord to the center of the 10cm radius circle, you get an equilateral triangle. Taking the altitude of that triangle with the base being the chord, you can find the altitude length to be equal to $5 sqrt3$. This attitude is also the radius of the inner circle as the chord is tangent to the inner circle and altitudes form right angles with the base.



    Thus, the thickness of the pipe is then $10 - 5 sqrt3 = 5(2-sqrt3)$, which is choice (E).






    share|cite|improve this answer

























      up vote
      1
      down vote













      Given that the cut is just through the wall of the pipe, that means on the outside circle of diameter 20cm, and thus radius 10cm, it has a chord of length 10cm such that the chord is also tangent to the inner circle.



      If you draw that chord and draw two segments connecting either endpoint of the chord to the center of the 10cm radius circle, you get an equilateral triangle. Taking the altitude of that triangle with the base being the chord, you can find the altitude length to be equal to $5 sqrt3$. This attitude is also the radius of the inner circle as the chord is tangent to the inner circle and altitudes form right angles with the base.



      Thus, the thickness of the pipe is then $10 - 5 sqrt3 = 5(2-sqrt3)$, which is choice (E).






      share|cite|improve this answer























        up vote
        1
        down vote










        up vote
        1
        down vote









        Given that the cut is just through the wall of the pipe, that means on the outside circle of diameter 20cm, and thus radius 10cm, it has a chord of length 10cm such that the chord is also tangent to the inner circle.



        If you draw that chord and draw two segments connecting either endpoint of the chord to the center of the 10cm radius circle, you get an equilateral triangle. Taking the altitude of that triangle with the base being the chord, you can find the altitude length to be equal to $5 sqrt3$. This attitude is also the radius of the inner circle as the chord is tangent to the inner circle and altitudes form right angles with the base.



        Thus, the thickness of the pipe is then $10 - 5 sqrt3 = 5(2-sqrt3)$, which is choice (E).






        share|cite|improve this answer













        Given that the cut is just through the wall of the pipe, that means on the outside circle of diameter 20cm, and thus radius 10cm, it has a chord of length 10cm such that the chord is also tangent to the inner circle.



        If you draw that chord and draw two segments connecting either endpoint of the chord to the center of the 10cm radius circle, you get an equilateral triangle. Taking the altitude of that triangle with the base being the chord, you can find the altitude length to be equal to $5 sqrt3$. This attitude is also the radius of the inner circle as the chord is tangent to the inner circle and altitudes form right angles with the base.



        Thus, the thickness of the pipe is then $10 - 5 sqrt3 = 5(2-sqrt3)$, which is choice (E).







        share|cite|improve this answer













        share|cite|improve this answer



        share|cite|improve this answer











        answered Aug 6 at 6:14









        Stone

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