My Math Forum intersection of diagonals of a trapezoid

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 June 26th, 2011, 08:43 PM #1 Newbie   Joined: Jun 2011 Posts: 2 Thanks: 0 intersection of diagonals of a trapezoid I have an isosceles trapezoid, of which I know the following information: the lenght of sides, long base and diagonals. How can I find the shorter base and the height? I have been trying to find similar triangles, but everytime I do it seems that they both have too many unknowns to help. What am I missing? Is there something that can help me about where the diagonals intersect? Thanks for any help!!
 June 26th, 2011, 10:38 PM #2 Senior Member   Joined: Apr 2007 Posts: 2,140 Thanks: 0 a, b, c, d and h are shorter base, diagonals, sides, long base and height respectively. $a\,=\,\frac{b^2-c^2}{d}$ $h\,=\,\frac{\sqrt{4c^2\,-\,(d-a)^2}}{2}\,=\,\frac{\sqrt{4c^2\,-\,(d-\frac{b^2-c^2}{d})^2}}{2}$
 June 27th, 2011, 12:57 PM #3 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,599 Thanks: 941 Math Focus: Elementary mathematics and beyond Re: intersection of diagonals of a trapezoid Since an isoceles trapezoid is a cyclic quadrilateral, Ptolemy's theorem may be of interest: http://en.wikipedia.org/wiki/Cyclic_...eral#Diagonals

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# height of trapezoid diagonal intersection

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