Results 1 to 4 of 4

Math Help - Circle GCSE Challenge - Help needed

  1. #1
    Newbie
    Joined
    Jul 2009
    Posts
    3

    Circle GCSE Challenge - Help needed

    Hello guys,

    I put this in the wrong forum previously, so I apologise if you have seen this post before.

    I've been trying to figure where to start with this, but no luck. I need help with this, because I've been at it for a while. I hope you understand what I'm getting at.

    Here it is:

    Q) The large circle has a radius of 10cm. Within the large circle are 4 smaller circles as shown in the link below (the image on the far left). 'You may have to click on the image for the picture to be clear so you can see what I mean.' Find the radius of the largest circle which will fit in the middle.



    http://mathworld.wolfram.com/images/...rcles_1000.gif
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by mathstudent View Post
    Hello guys,

    I put this in the wrong forum previously, so I apologise if you have seen this post before.

    I've been trying to figure where to start with this, but no luck. I need help with this, because I've been at it for a while. I hope you understand what I'm getting at.

    Here it is:

    Q) The large circle has a radius of 10cm. Within the large circle are 4 smaller circles as shown in the link below (the image on the far left). 'You may have to click on the image for the picture to be clear so you can see what I mean.' Find the radius of the largest circle which will fit in the middle.
    1. I'll show you how to calculate the radius of the inner circle using the drawing with 5 smaller circles.

    2. The tangent points of the smaller circles with the outer circle produce a regular pentagon. Let R denot the radius of the outer circle then the side of the pentagon is calculated as:

    s =  2 \cdot R \cdot \sin\left(\dfrac{180^\circ}{\underbrace{5}_{number  \ of\ circles}}\right)

    3. Use proportion in the indicated isosceles triangle:

    \dfrac sR=\dfrac {2r}{R-r} \implies \boxed{r=\dfrac{sR}{2R+s}}

    4. The radius of the innermost circle, touching the smaller circle, is

    \rho=R-2r

    5. This method can be used with all other examples where more than 2 circles are surrounded by one big circle. You only have to change the number of circles in the equation at 2.
    Attached Thumbnails Attached Thumbnails Circle GCSE Challenge - Help needed-innererkreis.png  
    Last edited by earboth; July 29th 2009 at 10:32 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Jun 2009
    Posts
    660
    Thanks
    133
    Join the centres of the small circles to form a square and extend one of its diagonals to form a diameter of the large circle. Call the radius of a small circle  R and calculate the length of the diagonal and hence the diameter of the large circle in terms of  R . Put this equal to 20cm.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Jul 2009
    Posts
    3
    Thank you so much! Life saver!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Probability GCSE
    Posted in the Statistics Forum
    Replies: 4
    Last Post: November 14th 2010, 02:41 PM
  2. Replies: 5
    Last Post: April 29th 2010, 05:40 AM
  3. Circle GCSE Challenge - Help needed
    Posted in the Math Puzzles Forum
    Replies: 1
    Last Post: July 29th 2009, 10:06 AM
  4. Circle help needed
    Posted in the Geometry Forum
    Replies: 6
    Last Post: July 9th 2007, 10:51 AM
  5. GCSE Maths
    Posted in the Math Forum
    Replies: 1
    Last Post: August 21st 2006, 07:54 AM

Search Tags


/mathhelpforum @mathhelpforum