Okay, with the #MathsEd crowd here, let's do some Sunday night #mathscpd !

I teach IGCSE and so teach the intersecting chords theorem. This says that if chords \( A B\) and \( CD\) intersect at a point \(P\) (possibly outside the circle) then \( AP \times PB= CP \times PD \). Often, the lengths are given in such a way that we set up a quadratic. For example, if \( x= AP\) and \(AB= 9\) we could end up with \(x(9-x)= 18\).

Conventional techniques then say to expand this to a quadratic, which would be \(x^2 -9x +18=0\), and then factorising and solving it, which involves finding two numbers that add to \(-9\) and multiply to \(18\).

But that's exactly what the equation \(x(9-x)= 18\) describes! So why bother multiplying out and rearranging in the first place?

Maybe a better approach would be to view \(x(9-x)= 18\) as the canonical form in the first place!

Well, I’m not sure about being an #edutooter yet, but here goes… I will miss my Twitter Maths community if it all goes up in 🔥 but really hope I can find you all again here! #introduction #maths #mathscpd #mathscpdchat #mathstlp