Help on 2008 O level amaths question

• Han chiang

  14 Sep 09, 20:50

  x-Coordinate of A is 4+3sqrt3

  x-Coordinate of B is 4-3sqrt3

  Please help me. I try for a long time still cant get it. I found eqn of AB and sub into C1 but cannot get.

  Any tips on how to do "proof/show that" questions? They are the hardest in Amaths...

  Thanks!

• Han chiang

  14 Sep 09, 20:58

  Woops its question 11. Why no picture come out de o.o

  [IMG]http://i978.photobucket.com/albums/ae263/hanchiang2/2008OLevelAmaths-1.jpg[/IMG]

• Han chiang

  14 Sep 09, 21:17

  Ok nvm I dont know how to post the picture here so I type it out.

  there is a circle, C1, which has its centre at the origin O. Another smaller circle, C2, passes through origin and has centre at Q. The point P(8,-6) lies on both circles and OP is a diameter of C2.

  The line through Q perpendicular to OP meets the circle C1 at the points A and B.

  So the question is...

  Show that the x-coordinate of A and B are a+bsqrt3 and a-bsqrt3 respectively, where a and b are integers to be found.

  For convenience, eqn of C1 is x^2 + y^2 = 100

                                 eqn of C2 is x^2 + y^2 -8x + 6y = 0

   

  Since I am asking for help, I would like to ask another simple question on geometry.

  There is a parallelogram ABCD.

  I wanna ask:

  1) Diagonals intersect at midpoints?

  2) midpoint of AC = midpoint of BD?

  3) Perpendicular distance from B to AC is ???

  Now a rhombus:

  1) Diagonals intersect at midpoints?

  2) all 4 sides are same?

  3) can be broken down into 4 same isosceles triangles?

  4) Diagonals are perpendicular?

  5) Midpoint of AC = midpoint of BD?

  I think thats all I have to ask. My concept on geometry stuffs are quite weak..

  Thanks for your time.

   

   

   

• dkcx

  14 Sep 09, 21:24

  Originally posted by Han chiang:

  
  1) Diagonals intersect at midpoints? Yes

  2) midpoint of AC = midpoint of BD? Yes

  3) Perpendicular distance from B to AC is ??? How to calculate depends on question and what you are given

  Now a rhombus:

  1) Diagonals intersect at midpoints? Yes

  2) all 4 sides are same? Yes

  3) can be broken down into 4 same isosceles triangles? No, the 2 lines inside might not always be same length

  4) Diagonals are perpendicular? Yes

  5) Midpoint of AC = midpoint of BD? Yes

  I think thats all I have to ask. My concept on geometry stuffs are quite weak..

  Thanks for your time.

   

   

• OHSheet

  14 Sep 09, 21:43

  

   

  post for you TS

• OHSheet

  14 Sep 09, 22:19

  alright TS. I'll post my solutions for Qn 11.

  for parts 1 and 2

  

  for part 3

  

  please let me know if it helps. All the best for your Os.

• Han chiang

  16 Sep 09, 13:39

  Omg thank you! Don't know why i sub in AB into C1 still cannot. Now can liao.

• OHSheet

  16 Sep 09, 17:08

  Originally posted by Han chiang:

  Omg thank you! Don't know why i sub in AB into C1 still cannot. Now can liao.

  right. All the best.