E maths *urgent* (question on triangle and semicircle)

• bonkysleuth

  6 Jul 09, 18:29

  In the diagram, the circle with centre at B has a radius (2r + 1) cm. The semicircle with centre at A and the semicircle with centre at C are identical and each has a radius (12-6r)cm. O is the centre of the largest semicircle.

  By using pythagoras theorem, form an equation in r and show that it reduces to 18r^2 - 57r + 42 = 0

  The questions before this were to find an expression in terms of r for BC and BO. (for guiding purposes)

  

  I need help with this question asap. a big thankssssssssssss!

   

  p.s - sorry for the distorted pic

• wee_ws

  6 Jul 09, 18:47

  Hi,

    Your circles should meet when you draw them :P

    BC = (2r + 1) + (12 - 6r) = 13 - 4r.

    OB = 2(12 - 6r) - (2r + 1) = 23 - 14r.

    OC = 12 - 6r.

    Now OB^2 + OC^2 = BC^2, based on the suggestion.

    Finally, the result holds upon expansion and simplification.

    Thanks!

  Cheers,
  Wen Shih