View source for Intersecting Chords

[[File:ChordTheorem.jpg|300px|right]]
This theorem relates to a characteristic of a [http://en.wikipedia.org/wiki/Cyclic_quadrilateral#Characterizations '''cyclic quadlitateral'''], the diagonals of which are two intersecting chords of the circumscribing circle.


The [http://www.mathopenref.com/chordsintersecting.html  '''Intersecting Chords Theorem'''] states that the relationship '''''(ao x ob = co x od)''''' is true for <u>'''any'''</u> two intersecting chords, whether or not one of them is a diameter.

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| '''Measuring Beam Deflections'''
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The theorem can be useful when measuring the radius of bending of a deflected beam if one of the chords is taken to be the length of the beam
e.g.
* set up a strip of material as a simple beam
* note the distance between supports '''''(cd)'''''
* apply a central load to make it bend - or '''''[[Beam Deflection|‘deflect’(Δ)]]''''' - therefore '''co = od = ½cd'''
* measure the deflection '''''(ob)'''''
Bending Radius ''(R)'' can be calculated as follows:
* ao x ob = co x od
* (2R-Δ) x Δ = ½cd x ½cd
* but, for small deflections, Δ<sup>2</sup> will be negligible
* so R = cd<sup>2</sup> ÷ 8 x Δ
''(see ‘Structures’ by [http://en.wikipedia.org/wiki/J.E._Gordon J.E.Gordon] ISBN  0 14 02.1961 7)'' </span>
|[[File:DeflectedBeamChords.jpg|400px|right]]
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[[Category:Secondary]]
[[Category:Structures]]
[[Category:Terminology]]