# Thread: Find the length of da diagonal in a quadrilateral

1. ## Find the length of da diagonal in a quadrilateral

Hai,

i have 3 points on a plane, whose positions are fixed. and
one arbitrary point, it's position can vary.

i have to form a quadrilateral by making use of these 4
points , it may form concave or convex quadrilateral.

from this data one point is clear that 2 sides and 1
diagonal length are fixed. and i want to calculate the
length of another diagonal.

how do i do it??

thanks !!
Ashwini

2. Originally Posted by vd.ashwini@yahoo.co.in
Hai,

i have 3 points on a plane, whose positions are fixed. and
one arbitrary point, it's position can vary.

i have to form a quadrilateral by making use of these 4
points , it may form concave or convex quadrilateral.

from this data one point is clear that 2 sides and 1
diagonal length are fixed. and i want to calculate the
length of another diagonal.

how do i do it??

thanks !!
Ashwini
Why don't you give us the 3 given points. Then we could play with them.

3. thanks for ur replay .....
3 points are known and which are
A (0,0)
B (0,b)
C (c,0) and
D (which is arbitrary and can any where in the quadrant and can be within triangle ABC or may be outside also. if it is inside the triangle then forms concave quadrilateral ABCD, if outside then makes convex quadrilateral ABCD)

hope this gives clear idea now,
i want to calculate the length if the diagonals, how do i do it.

regards,
Ashwini

4. yes, one diagonal is fixed.. the other one is computed as the distance between the point $(x,y)$ and the origin, isn't it?

5. Thank u very much for ur replay,
Basically what u are telling is correct, but i am intended
to calculate the angle between diagonal AD and x-axis.

The distance between BD and CD are keep changing and i will
be getting proportional length. (But line of sight will be
on the same line)

So what i thought is once i get proportional length of AD i
will calculate angle between AD and x-axis. And this wont
get affected even if BD and CD varies on the LOS.

(refer the figure bellow ..)

Thanks !
Ashwini

|
|A(0,0) B
- |--------(*)------------------------------------
| /
| /
| /
| /
| /
| /
| /
| / (*)-(arbitrary point)
(*)C D
|
|
|

6. so basically, you only need the angle

$\theta = \tan^{-1}\left(\frac{y}{x}\right)$..

is that it?

7. In case if it forms rt angled triangle then the formula given by u holds good, but the thing is always it wont form rt angles triangle.

It is known that one diagonal is fixed and length is known, i want to calculate the length of another diagonal for the given sides of quadrilateral.

Thanks !
Ashwini

8. you can always form a right triangle with the points O, (x,y) and a point on the x-axis as long as AB and AC is a side of the quadrilateral..

see attach pic..

9. Thanks for ur replay..

i got ur idea .. and tried like this:
(using distance formula)
d1^2 = x^2+b^2+y^2 - 2*b*y
d2^2 = c^2+x^2+y^2 - 2*c*x

when i solve above two equations i got the answer as follows:
d1^2 - d2^2 = b^2-c^2-2*(b*y-c*x)

in this equation also there are 2 unknowns, how to solve ..........??

Thanks !!

10. first, what do you really want to solve?

11. yes ... i am struggling to solve this from a month ...

if possible plz help me ........

12. yes .. it is very urgent for me to solve this ..
plz help me .....

13. i min, you state the whole problem as stated..

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### diagonal length of quadrilateral

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