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    I’ve spent several hours on this problem trying to attack it different ways and I finally got to a conclusion (or 2). I got 2 answers for the problem so was hoping if anyone could check my work (and tell me if I’ve gone wrong or if it’s correct) or perhaps work it out themselves and then compare answers?

    This problems really bugged me and I just feel like I’ve gone wrong. I’ve labelled my working out in stages so hopefully you can follow it.

    Thanks


    This is the question
    Name:  20D636F4-D394-470D-B30D-4C0344478E61.jpg.jpeg
Views: 20
Size:  28.3 KB
    Here is my workings:
    https://imgur.com/a/rF82L
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    (Original post by Y11_Maths)
    I’ve spent several hours on this problem trying to attack it different ways and I finally got to a conclusion (or 2). I got 2 answers for the problem so was hoping if anyone could check my work (and tell me if I’ve gone wrong or if it’s correct) or perhaps work it out themselves and then compare answers?

    This problems really bugged me and I just feel like I’ve gone wrong. I’ve labelled my working out in stages so hopefully you can follow it.

    Thanks


    This is the question
    Name:  20D636F4-D394-470D-B30D-4C0344478E61.jpg.jpeg
Views: 20
Size:  28.3 KB
    Here is my workings:
    https://imgur.com/a/rF82L
    Can you please post what answer so I can compare it with mine? It's not clear from your working what your final answer was.
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    (Original post by Y11_Maths)
    I’ve spent several hours on this problem trying to attack it different ways and I finally got to a conclusion (or 2). I got 2 answers for the problem so was hoping if anyone could check my work (and tell me if I’ve gone wrong or if it’s correct) or perhaps work it out themselves and then compare answers?

    This problems really bugged me and I just feel like I’ve gone wrong. I’ve labelled my working out in stages so hopefully you can follow it.

    Thanks


    This is the question
    Name:  20D636F4-D394-470D-B30D-4C0344478E61.jpg.jpeg
Views: 20
Size:  28.3 KB
    Here is my workings:
    https://imgur.com/a/rF82L
    The point (r-9, r-8) lies on the circle.

    \therefore (r-8)^2+(r-9)^2=r^2 \therefore r=17 \pm 12

    From the diagram, we need to take r=29.
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    (Original post by RogerOxon)
    The point (r-9, r-8) lies on the circle.

    \therefore (r-8)^2+(r-9)^2=r^2 \therefore r=17 \pm 12

    From the diagram, we need to take r=29.
    Yep I just spotted that. Going to absolutely cry myself to sleep tonight! What an absolute mug I feel, thanks.
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    (Original post by RogerOxon)
    The point (r-9, r-8) lies on the circle.

    \therefore (r-8)^2+(r-9)^2=r^2 \therefore r=17 \pm 12

    From the diagram, we need to take r=29.
    So where actually did I go wrong in my workings(assuming there is more than 1 way to work it out)? Since I was only 1 away from the answer...?
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    (Original post by Y11_Maths)
    Yep I just spotted that. Going to absolutely cry myself to sleep tonight! What an absolute mug I feel, thanks.
    Whilst it's good that you have a solution. It's important to know why your own working failed.

    From what I can tell of your image in imgur, you've assumed that a line from the centre to the corner passes through the corner of the small oblong, which is not the case.

    Here's an exagerated blow-up.
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    (Original post by Y11_Maths)
    So where actually did I go wrong in my workings(assuming there is more than 1 way to work it out)? Since I was only 1 away from the answer...?
    Have you assumed that there is a straight line that passes through the two corners of the rectangle and to the centre of the circle? Remember that this is a rectangle (9x8) not a square so this isn't the case here.

    ghostwalker beat me and his post is inifinitely better since it contains a diagram
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    (Original post by ghostwalker)
    Whilst it's good that you have a solution. It's important to know why your own working failed.

    From what I can tell of your image in imgur, you've assumed that a line from the centre to the corner passes through the corner of the small oblong, which is not the case.

    Here's an exagerated blow-up.
    Yeah I was wondering where’re I was allowed to do that or not. Thanks for pointing that out. Would my method have worked if it was a square in the corner instead of an oblong or would it not make a difference?
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    (Original post by Notnek)
    Have you assumed that there is a straight line that passes through the two corners of the rectangle and to the centre of the circle? Remember that this is a rectangle (9x8) not a square so this isn't the case here.

    ghostwalker beat me and his post is inifinitely better since it contains a diagram
    Yes I did
    On one hand I feel great for actually having the initiative to do that and follow through with my method to get a final answer which was less than 1 away from the correct answer so I’m kinda proud. But on the other hand I feel so dumb for not noticing it could be done in about 2 minutes (not 5 hours) and there was a slight flaw in my method. I think I deserve style points though
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    (Original post by Y11_Maths)
    Would my method have worked if it was a square in the corner instead of an oblong or would it not make a difference?
    Your method might have worked if it was a square - difficult to tell. It's rather torturous trying to follow what you've done. I stopped when I realised the first error.

    Looking further, when you "squared both sides" you've missed all the cross terms on the right hand side and got a sign wrong. You need to brush up your algebra!
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    (Original post by ghostwalker)
    Your method might have worked if it was a square - difficult to tell. It's rather torturous trying to follow what you've done. I stopped when I realised the first error.

    Looking further when you "squared both sides" you've missed all the cross terms on the right hand side and got a sign wrong. You need to brush up your algebra!
    Oh do you mean put everything on the right side into brackets and then square instead of individually squaring each term?
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    (Original post by Y11_Maths)
    Oh do you mean put everything on the right side into brackets and then square instead of individually squaring each term?
    That would do it.

    You treat the side of the equation as one thing and apply the appropriate function to that. Be it, squaring, exponetiating, taking the sine of it, etc.
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    (Original post by ghostwalker)
    That would do it.

    Yes you treat the side of the equation as one thing and apply the appropriate function to that. Be it, squaring, exponetiating, taking the sine of it, etc.
    Understood! Thanks for the help
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    (Original post by Y11_Maths)
    Yep I just spotted that. Going to absolutely cry myself to sleep tonight! What an absolute mug I feel
    (Original post by Y11_Maths)
    On one hand I feel great for actually having the initiative to do that and follow through with my method to get a final answer which was less than 1 away from the correct answer so I’m kinda proud. But on the other hand I feel so dumb for not noticing it could be done in about 2 minutes (not 5 hours) and there was a slight flaw in my method. I think I deserve style points though
    You should be proud that you spent so long on it before asking for help - striving to understand, and practicing, are what will improve your understanding and accuracy.

    I didn't have time to look at your method earlier. From the labeling of the diagram, I think that it would have worked, had the shape in the corner been a square. However, the generic approach of using the equation of a circle is just as easy, and works for all situations.

    Always double-check your answer by substituting it back into your first equation, or a related one. On some exams, you might also know that the numbers will be 'nice'.
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    (Original post by RogerOxon)
    You should be proud that you spent so long on it before asking for help - striving to understand, and practicing, are what will improve your understanding and accuracy.

    I didn't have time to look at your method earlier. From the labeling of the diagram, I think that it would have worked, had the shape in the corner been a square. However, the generic approach of using the equation of a circle is just as easy, and works for all situations.

    Always double-check your answer by substituting it back into your first equation, or a related one. On some exams, you might also know that the numbers will be 'nice'.
    Yeah thanks. Although I did get a little confused because my value for x as 8+sqrt145 fit into the first line on step 4 and was the same outcome on both sides of the equation whereas it did not work for other values of x :/
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