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 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 ‘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, Δ2 will be negligable
so R = cd2 ÷ 8 x Δ