Results 1 to 2 of 2

Math Help - Two non-intersecting circles...

  1. #1
    Newbie
    Joined
    Jan 2014
    From
    Brazil
    Posts
    1

    Unhappy Two non-intersecting circles...

    Two non-intersecting circles C1, containing points M and S, and C2, containing points N and R, have centres P and Q where PQ=50. The line segments [MN] and [SR] are common tangents to the circles. The size of the reflex angle MPS is α, the size of the obtuse angle NQR is β, and the size of the angle MPQ is θ. The arc length MS is l1and the arc length NR is l2. The radius C1 is x, where x is greater or equal to 10 and the radius of C2 is 10.

    (a) Explain why x>40.
    ---> Because if the radius of C2 is 10, then PQ minus this radius is 40. If the radius of C1 exceeds 40, then PQ would not make sense and it would have to have another value.

    (b) Show that cosθ = (x-10)/50.

    (c) (i) Find an expression for MN in terms of x.
    (i) Find the value of x that minimises MN.

    (d) Find an expression in terms of x for:
    (i) α;
    (ii) β.

    (e) The length of the perimeter is given by l1+l2+MN+SR.
    (i) Find an expression, b(x), for the length of the perimeter in terms of x.
    (ii) Find the maximum value of the length of the perimeter.
    (iii) Find the value of x that fives a perimeter of length 200.



    Please help; any contribution would be a lot of help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Dec 2012
    From
    Athens, OH, USA
    Posts
    613
    Thanks
    249

    Re: Two non-intersecting circles...

    Hi,
    The attachment shows some answers together with a diagram that should help you when x > 10. Of course, the min and max questions probably involve calculus. Warning hint: the answers to the last two questions on the perimeter are a little tricky.

    Two non-intersecting circles...-mhfcalc28.png
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Non intersecting circles...
    Posted in the Geometry Forum
    Replies: 2
    Last Post: September 29th 2011, 12:23 PM
  2. Intersecting Circles
    Posted in the Geometry Forum
    Replies: 1
    Last Post: May 7th 2011, 04:07 PM
  3. Intersecting Circles
    Posted in the Geometry Forum
    Replies: 2
    Last Post: March 26th 2011, 11:16 PM
  4. Two circles intersecting each other...
    Posted in the Geometry Forum
    Replies: 2
    Last Post: February 25th 2010, 10:32 AM
  5. intersecting circles
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: March 14th 2009, 12:22 AM

Search Tags


/mathhelpforum @mathhelpforum