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February 12th, 2011, 07:11 PM   #1
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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.
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February 12th, 2011, 07:51 PM   #2
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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.
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February 13th, 2011, 01:52 AM   #3
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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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