1. circle geometry help 4

http://www.boardofstudies.nsw.edu.au...hs_ext1_05.pdf

with explanation and reasons please question 3d

2. What do you specifically do not understand?

3. Originally Posted by spruancejr
What do you specifically do not understand?
i have trouble giving the reasons in circle geometry can you or somebody else help me.its just question 3d

4. Originally Posted by andy69
i have trouble giving the reasons in circle geometry can you or somebody else help me.its just question 3d
When the two chords Ab and CD intersect each other at E, they satisfy the following condition.

$\frac{AE}{EB} = \frac{CE}{ED}$ .............(1)

AE = 4, AB = 7. So EB = ...?

CD = l, ED = x, so CE = ...?

Substitute these values in equation (1) and simplify.

The equation obtained is

$x^2 - lx + 12 = 0.$ Or

$l = x + \frac{12}{x}$

To get the minimum length of the chord CD, find dl/dx and equate it to zero. Then solve for x. Substitute this value in eq.(1) to find CF, then find CD.

5. Originally Posted by sa-ri-ga-ma
When the two chords Ab and CD intersect each other at E, they satisfy the following condition.

$\frac{AE}{EB} = \frac{CE}{ED}$ .............(1)

AE = 4, AB = 7. So EB = ...?

CD = l, ED = x, so CE = ...?

Substitute these values in equation (1) and simplify.

The equation obtained is

$x^2 - lx + 12 = 0.$ Or

$l = x + \frac{12}{x}$

To get the minimum length of the chord CD, find dl/dx and equate it to zero. Then solve for x. Substitute this value in eq.(1) to find CF, then find CD.
im really sorry about this but im not sure what to do im not very good at circle geometry because my teacher was absent for most of this whole topic and know i have a test about it, again im really sorry can you explain it abit more.

6. Originally Posted by andy69
im really sorry about this but im not sure what to do im not very good at circle geometry because my teacher was absent for most of this whole topic and know i have a test about it, again im really sorry can you explain it abit more.
Open any text book and find the properties of the circle. For that there is no need of any teacher.

7. Originally Posted by sa-ri-ga-ma
When the two chords Ab and CD intersect each other at E, they satisfy the following condition.

$\frac{AE}{EB} = \frac{CE}{ED}$ .............(1)

AE = 4, AB = 7. So EB = ...?

CD = l, ED = x, so CE = ...?

Substitute these values in equation (1) and simplify.

The equation obtained is

$x^2 - lx + 12 = 0.$ Or

$l = x + \frac{12}{x}$

To get the minimum length of the chord CD, find dl/dx and equate it to zero. Then solve for x. Substitute this value in eq.(1) to find CF, then find CD.
EB=3 how can you get CE when theres 2 unknowns the fraction would just be 4/3=CE/X

8. Originally Posted by andy69
EB=3 how can you get CE when theres 2 unknowns the fraction would just be 4/3=CE/X
CE = CD - ED = (l - x)

9. Originally Posted by sa-ri-ga-ma
CE = CD - ED = (l - x)
ok so 4/3=(l-x)/x
cross multiply
4x=3(l-x)
4x=3l-3x
4x+3x=3l
7x=3l
x=3l/7

now do i sub this answer into the 2nd equation that you said

10. Originally Posted by andy69
now do i sub this answer into the 2nd equation that you said
I think it's time you be told that you need classroom help;
we can't replace your teacher here...

11. Originally Posted by andy69
ok so 4/3=(l-x)/x
cross multiply
4x=3(l-x)
4x=3l-3x
4x+3x=3l
7x=3l
x=3l/7

now do i sub this answer into the 2nd equation that you said
Sorry.

The expression should be

AE*EB = CE*ED

12. Originally Posted by sa-ri-ga-ma
Sorry.

The expression should be

AE*EB = CE*ED
(4)x(3)= x(l - x)
7=xl-x^2
x^2+7=xl
x^2+7/x=l
so after this i should sub it into any two of those equations?

13. Originally Posted by andy69
(4)x(3)= x(l - x)
7=xl-x^2
x^2+7=xl
x^2+7/x=l
so after this i should sub it into any two of those equations?
What is 4X3 ?

What is 4 + 3 ?

14. Originally Posted by sa-ri-ga-ma
What is 4X3 ?

What is 4 + 3 ?
* this sign is times isnt it.
12=xl-x^2
12+x^2=xl
12+x^2/x=l sorry i miscalculated.

15. Originally Posted by andy69
* this sign is times isnt it.
12=xl-x^2
12+x^2=xl
12+x^2/x=l sorry i miscalculated.
12+x^2/x=l

Write the above equation as

(12/x) + x = l.
Find dl/dx and equate it to zero. Then solve for x. You know the relation between x and l. Hence find the minimum length of the chord.