scalene trapezoid point of diagonals intersection
We have a scalene trapezoid. We know AB and CD bases and the diagonal AC. Be P the point of intersection of the two diagonals. Is it possible to find the general expression for AP?I would like to know the formula for AP, if it exists, depending on AB, CD, AC
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$\begingroup$Here are some hints.
- Which line segments are the diagonals?
- Since you know two points on each diagonal, you can write an equation for each of the diagonals.
- Solve for the point that is contained in both diagonals.
Let me re-link the diagram you have provided : trapezoid.
No, it is not enough to know $ AB, CD $ and $ AC $ to calculate $ AP $. Try to think of the three segments $ DC, CA $ and $ AB $ as "rods" with "hinges" at points $ C $ and $ A $. You can deform this linkage in anyway you wish, except for preserving the lengths of the rods and the property that $ AB \parallel CD $. It is easy to see the many variations of trapezoids you can form so, each having a different value for $ AP $ but all have the same $ AB, CD $ and $ AC $.
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