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 February 12th, 2011, 07:11 PM #1 Newbie   Joined: Feb 2011 Posts: 1 Thanks: 0 Geometry Question Find the distance between the vertices at the right angles when two 3-4-5 right triangles are put together to form a cyclic quadrilateral. I think this is stating that Two 3-4-5 right traingles are put together to form a cyclic quadrilateral. So the two triangles have side 3 , 4 , 5 . Find the distance between the vertices at the right angles. I'm really unsure on what to start with here.
 February 12th, 2011, 07:51 PM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Geometry Question In a cyclic quadrilateral, opposite angles are supplementary, so the two right angles of the triangles must be opposite one another, producing a rectangle whose diagonal is the hypotenuses of the triangles, which is a distance of 5 units.
 February 13th, 2011, 01:52 AM #3 Senior Member     Joined: Feb 2010 Posts: 711 Thanks: 147 Re: Geometry Question ... or if the sides are consecutively 3,3,4,4 (instead of 3,4,3,4), the distance between the right angles is 4.8.

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