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Find the large base of trapezoid, with diagonals length 6 and 8, if the angle between them is 90 degrees. Actually the original problem asks to find the length of the line parallel to the base, that goes through the intersection points of the diagonals. I calculated the expression in terms of 2 bases (the harmonic ratio of trapezoid), i have also calculated (a+b), where a and b are the bases. But i need to find a*b.

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    $\begingroup$ A couple of sketches will show that knowing that the diagonals have length $6$ and $8$ and meet at right angles is not sufficient to determine the larger (or smaller) base. $\endgroup$ Feb 2 '16 at 16:08
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The reason you are having a hard time is that the question you ask has multiple answers. That is, the lengths of two orthogonal diagonals in a trapezoid do not determine the lengths of the bases.

For example, let the diagonals $AB$ and $CD$ be two lines of length $6$ and $8$ respectively, meeting at a point which is $1$ away from $A$ and $\frac{4}{3}$ away from $C$. Then the length of base $BD$ is $\frac{25}{3}$.

Now let the two diagonals meet at a point which is $3$ away from $A$ and $4$ away from $C$. Then the length of base $BD$ is $5$.

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