Need to solve Isosceles trapezoid diagonal intersection problem

abehil

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An isosceles trapezoid.
Code:
          A      y     B

                 X

   D             z             C

There are two diagonals AC and DB. They intersect at X.
I can find the length of the diagonals just fine.
I need help calculating AX.

Sample: AB=12, DC=20, yz=40 How do I find AX?

Edited for clarity: y=AB/2, z=DC/2
 
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An isosceles trapezoid.
Code:
          A      y     B

                 X

   D             z             C
Sample: AB=12, DC=20, yz=40 How do I find AX?
I can find the length of the diagonals just fine. But I need to know the value of AX.
I've seen some formulas about getting yX which doesn't help find AX.

What do you know about the location of X - inside the trapezoid?
 
Please show your work in calculating above. Thank you.

When you posted that problem here:
http://www.sosmath.com/CBB/viewtopic.php?f=1&t=67951
you had the diagonals crossing at right angles...changed your mind?

Denis,

I didn't change the problem, just refined it as I figured out that I was dealing with an isosceles trapezoid, just like the topic name says.
I don't have any work to show, my entire post asks a question. One specific question.

I'm sorry but I have no idea what your version of the diagram is meant to say. I'll state clearly what mine says if that helps.
This is an isosceles trapezoid with diagonals AC and DB that intersect at the X. Pretty simple.
It's true that in a text diagram the diagonals can't be drawn so please bare with me on that. And if the X looks a little askew please
forgive my text diagram, the X is supposed to be right in line with the two diagonals.
I do know how to calculate the length of the diagonals themselves so no need to cover that and no need to make that part of my question.

As I described above, I'm trying to find out how to calculate the length of AX. I can only supply 3 sample values.
I need a solution that shows how to calculate AX starting with only those 3 values. Those values are the length of the two bases and the distance between the bases.

Would you like to help?
 
YOU originally (link I supplied) posted this:
"The X forms two right triangles that overlap at the pivot point."
and this:
"Looking at the X shape, the top and bottom of the X form two triangles but they won't be the same size as each other and unlikely to have the same angles. Simply restated, bisecting the X horizontally results in two differently sized non-right triangles."

Asked you TWICE now if that still applies: DOES IT APPLY?

If it does, then bisecting horizontally this mysterious X results
in 45 degree angles...you don't seem to know this simple result.

AND you state that "top and bottom" of the X don't contain/form
equal angles: that's complete nonsense...

You keep stating you know how to calculate the diagonals:
again, SHOW HOW.

Denis,

I'm not asking this question as some sort of quiz that I know the answer to. I actually am looking for someone who KNOWS what the steps are in solving for AX.
Here is the formula I use to find the length of the diagonals.
AC2 = ( DC-AB + DC-AB/2)2 + yz2
 
Looking at the X shape, the top and bottom of the X form two triangles but they won't be the same size as each other and unlikely to have the same angles. Simply restated, bisecting the X horizontally results in two differently sized non-right triangles.

That would be incorrect.

Since we are dealing with trapezoids, those triangles are similar.[edited]

The sides of those triangles would be proportional.

Does that guide you to a solution?
 
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