Help on 2008 O level amaths question

Han chiang SG

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 SG

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 SG

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 SG

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 SG

post for you TS

OHSheet SG

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 SG

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

OHSheet SG

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

right. All the best.