Intersecting Chords

This theorem relates to a characteristic of a cyclic quadlitateral, the diagonals of which are two intersecting chords of the circumscribing circle.

It can be useful when measuring the radius of bending of a deflected beam, for example, if one of the chords is taken to be the length of the beam

File:DeflectedBeamChords.jpg

e.g.

1. set up a strip of material as a simple beam
2. note the distance between supports (cd)
3. apply a central load to make it bend - or ‘deflect’(Δ) - therefore co = od = ½cd
4. 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, Δ² will be negligible
• so R = cd² ÷ 8 x Δ

(see ‘Structures’ by J.E.Gordon ISBN 0 14 02.1961 7)