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What is the radius of the table?

  1. Oct 19, 2004 #1
    Anyone has any clue to these questions? They are from a contest last year.
    Please Help and if you don't mind... please explain in detail.. Thanks!

    1. A library has between 1000 and 2000 books. Of these, 25% are fiction, 1/13 are biographies and 1/17 are atlases. How many books are either biographies or atlases?

    2. A circular table is pushed into a corner of a rectangular room so that it touches both walls. A point on the edge of the table between the two points of contact is 2 inches from one wall and 9 inches from the other wall. What is the radius of the table?

    3. Let f(x) = ax + b, with b<a both positive integers. If for positive integers p and q, f(p) = 18 and f(q) = 39, what is the value of b?

    4. In Triangle SBC, SB = 12, BC = 15, and SC=18. Let O be the point for which BO bisects angle SBC and CO bisects angle SCB. IF M and L are on sides SB and SC respectively so that ML is parallel to side BC and contains point O, what is the perimeter of Triangle SML?
     
  2. jcsd
  3. Oct 19, 2004 #2

    Gokul43201

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    1. What number between 1000 and 2000 can be divided exactly by 4, 13 and 17 ?

    2. Let the co-ordinates of the point be [itex](rcos\theta, rsin\theta ) [/itex]. You now have 2 equations in 2 unknowns.

    3. Subtract the two equations. You get only 4 possible choices for the values of a. Three of these are ruled out by inspection - in fact, it's plain to see why. The surviving one works.

    4. Let SO extended meet BC at R. Since O is the incenter, we have (I'm not sure what this rule is called) SO/OR = (12+18)/15. From here, it's just similar triangles.
     
    Last edited: Oct 19, 2004
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