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 345 right triangles are put together to form a cyclic quadrilateral. I think this is stating that Two 345 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: 706 Thanks: 141  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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